1
|
Huang X, Shi W, Gao X, Wei X, Zhang J, Bian J, Yang M, Liu TY. LordNet: An efficient neural network for learning to solve parametric partial differential equations without simulated data. Neural Netw 2024; 176:106354. [PMID: 38723308 DOI: 10.1016/j.neunet.2024.106354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2023] [Revised: 02/23/2024] [Accepted: 04/29/2024] [Indexed: 06/17/2024]
Abstract
Neural operators, as a powerful approximation to the non-linear operators between infinite-dimensional function spaces, have proved to be promising in accelerating the solution of partial differential equations (PDE). However, it requires a large amount of simulated data, which can be costly to collect. This can be avoided by learning physics from the physics-constrained loss, which we refer to it as mean squared residual (MSR) loss constructed by the discretized PDE. We investigate the physical information in the MSR loss, which we called long-range entanglements, and identify the challenge that the neural network requires the capacity to model the long-range entanglements in the spatial domain of the PDE, whose patterns vary in different PDEs. To tackle the challenge, we propose LordNet, a tunable and efficient neural network for modeling various entanglements. Inspired by the traditional solvers, LordNet models the long-range entanglements with a series of matrix multiplications, which can be seen as the low-rank approximation to the general fully-connected layers and extracts the dominant pattern with reduced computational cost. The experiments on solving Poisson's equation and (2D and 3D) Navier-Stokes equation demonstrate that the long-range entanglements from the MSR loss can be well modeled by the LordNet, yielding better accuracy and generalization ability than other neural networks. The results show that the Lordnet can be 40× faster than traditional PDE solvers. In addition, LordNet outperforms other modern neural network architectures in accuracy and efficiency with the smallest parameter size.
Collapse
Affiliation(s)
- Xinquan Huang
- King Abdullah University of Science and Technology, Saudi Arabia.
| | | | | | | | - Jia Zhang
- Microsoft Research AI4Science, China.
| | | | - Mao Yang
- Microsoft Research AI4Science, China.
| | | |
Collapse
|
2
|
Drissi M, Keeble JWT, Rozalén Sarmiento J, Rios A. Second-order optimization strategies for neural network quantum states. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2024; 382:20240057. [PMID: 38910393 DOI: 10.1098/rsta.2024.0057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/31/2024] [Accepted: 05/13/2024] [Indexed: 06/25/2024]
Abstract
The Variational Monte Carlo (VMC) method has recently seen important advances through the use of neural network quantum states. While more and more sophisticated ansatze have been designed to tackle a wide variety of quantum many-body problems, modest progress has been made on the associated optimization algorithms. In this work, we revisit the Kronecker-Factored Approximate Curvature (KFAC), an optimizer that has been used extensively in a variety of simulations. We suggest improvements in the scaling and the direction of this optimizer and find that they substantially increase its performance at a negligible additional cost. We also reformulate the VMC approach in a game theory framework, to propose a novel optimizer based on decision geometry. We find that on a practical test case for continuous systems, this new optimizer consistently outperforms any of the KFAC improvements in terms of stability, accuracy and speed of convergence. Beyond VMC, the versatility of this approach suggests that decision geometry could provide a solid foundation for accelerating a broad class of machine learning algorithms. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.
Collapse
Affiliation(s)
- M Drissi
- TRIUMF , Vancouver, British Columbia V6T 2A3, Canada
| | - J W T Keeble
- Department of Physics, University of Surrey , Guildford, GU2 7XH, UK
| | - J Rozalén Sarmiento
- Departament de Física Quàntica i Astrofísica, Universitat de Barcelona (UB) , c. Martí i Franquès 1, Barcelona E08028, Spain
- Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB) , Barcelona, Spain
| | - A Rios
- Department of Physics, University of Surrey , Guildford, GU2 7XH, UK
- Departament de Física Quàntica i Astrofísica, Universitat de Barcelona (UB) , c. Martí i Franquès 1, Barcelona E08028, Spain
- Institut de Ciències del Cosmos (ICCUB), Universitat de Barcelona (UB) , Barcelona, Spain
| |
Collapse
|
3
|
Li X, Huang JC, Zhang GZ, Li HE, Shen ZP, Zhao C, Li J, Hu HS. Improved optimization for the neural-network quantum states and tests on the chromium dimer. J Chem Phys 2024; 160:234102. [PMID: 38884396 DOI: 10.1063/5.0214150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/16/2024] [Accepted: 05/30/2024] [Indexed: 06/18/2024] Open
Abstract
The advent of Neural-network Quantum States (NQS) has significantly advanced wave function ansatz research, sparking a resurgence in orbital space variational Monte Carlo (VMC) exploration. This work introduces three algorithmic enhancements to reduce computational demands of VMC optimization using NQS: an adaptive learning rate algorithm, constrained optimization, and block optimization. We evaluate the refined algorithm on complex multireference bond stretches of H2O and N2 within the cc-pVDZ basis set and calculate the ground-state energy of the strongly correlated chromium dimer (Cr2) in the Ahlrichs SV basis set. Our results achieve superior accuracy compared to coupled cluster theory at a relatively modest CPU cost. This work demonstrates how to enhance optimization efficiency and robustness using these strategies, opening a new path to optimize large-scale restricted Boltzmann machine-based NQS more effectively and marking a substantial advancement in NQS's practical quantum chemistry applications.
Collapse
Affiliation(s)
- Xiang Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jia-Cheng Huang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Guang-Ze Zhang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Hao-En Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Zhu-Ping Shen
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Chen Zhao
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jun Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
- Department of Chemistry and Guangdong Provincial Key Laboratory of Catalytic Chemistry, Southern University of Science and Technology, Shenzhen 518055, China
- Fundamental Science Center of Rare Earths, Ganjiang Innovation Academy, Chinese Academy of Sciences, Ganzhou 341000, China
| | - Han-Shi Hu
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| |
Collapse
|
4
|
Boffi NM, Vanden-Eijnden E. Deep learning probability flows and entropy production rates in active matter. Proc Natl Acad Sci U S A 2024; 121:e2318106121. [PMID: 38861599 PMCID: PMC11194503 DOI: 10.1073/pnas.2318106121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 05/01/2024] [Indexed: 06/13/2024] Open
Abstract
Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. They involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework to estimate the score of this density. We show that the score, together with the microscopic equations of motion, gives access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles. To represent the score, we introduce a spatially local transformer network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of active particles undergoing motility-induced phase separation (MIPS). We show that a single network trained on a system of 4,096 particles at one packing fraction can generalize to other regions of the phase diagram, including to systems with as many as 32,768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.
Collapse
Affiliation(s)
- Nicholas M. Boffi
- Courant Institute of Mathematical Sciences, New York University, New York, NY10012
| | - Eric Vanden-Eijnden
- Courant Institute of Mathematical Sciences, New York University, New York, NY10012
| |
Collapse
|
5
|
Kowalski K, Peng B, Bauman NP. The accuracies of effective interactions in downfolding coupled-cluster approaches for small-dimensionality active spaces. J Chem Phys 2024; 160:224107. [PMID: 38860680 DOI: 10.1063/5.0207534] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2024] [Accepted: 05/22/2024] [Indexed: 06/12/2024] Open
Abstract
This paper evaluates the accuracy of the Hermitian form of the downfolding procedure using the double unitary coupled cluster (DUCC) ansatz on the benchmark systems of linear chains of hydrogen atoms, H6 and H8. The computational infrastructure employs the occupation-number-representation codes to construct the matrix representation of arbitrary second-quantized operators, allowing for the exact representation of exponentials of various operators. The tests demonstrate that external amplitudes from standard single-reference coupled cluster methods that sufficiently describe external (out-of-active-space) correlations reliably parameterize the Hermitian downfolded effective Hamiltonians in the DUCC formalism. The results show that this approach can overcome the problems associated with losing the variational character of corresponding energies in the corresponding SR-CC theories.
Collapse
Affiliation(s)
- Karol Kowalski
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Bo Peng
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| | - Nicholas P Bauman
- Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99354, USA
| |
Collapse
|
6
|
Nakano K, Sorella S, Alfè D, Zen A. Beyond Single-Reference Fixed-Node Approximation in Ab Initio Diffusion Monte Carlo Using Antisymmetrized Geminal Power Applied to Systems with Hundreds of Electrons. J Chem Theory Comput 2024; 20:4591-4604. [PMID: 38788330 PMCID: PMC11171267 DOI: 10.1021/acs.jctc.4c00139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Revised: 05/05/2024] [Accepted: 05/09/2024] [Indexed: 05/26/2024]
Abstract
Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in Fermionic systems, the projection needs to be carried out while imposing antisymmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed, predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as single reference. In this paper, we propose a new approach, applicable to systems as large as the C60 fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (antisymmetrized geminal power wave function constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single-reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.
Collapse
Affiliation(s)
- Kousuke Nakano
- Center
for Basic Research on Materials, National
Institute for Materials Science (NIMS), Tsukuba, Ibaraki 305-0047, Japan
- International
School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Sandro Sorella
- International
School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Dario Alfè
- Dipartimento
di Fisica Ettore Pancini, Università
di Napoli Federico II, Monte S. Angelo, 80126 Napoli, Italy
- Department
of Earth Sciences, University College London, Gower Street, London WC1E 6BT, U.K.
- Thomas
Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, U.K.
| | - Andrea Zen
- Dipartimento
di Fisica Ettore Pancini, Università
di Napoli Federico II, Monte S. Angelo, 80126 Napoli, Italy
- Department
of Earth Sciences, University College London, Gower Street, London WC1E 6BT, U.K.
| |
Collapse
|
7
|
Aldossary A, Campos-Gonzalez-Angulo JA, Pablo-García S, Leong SX, Rajaonson EM, Thiede L, Tom G, Wang A, Avagliano D, Aspuru-Guzik A. In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2024:e2402369. [PMID: 38794859 DOI: 10.1002/adma.202402369] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Revised: 04/28/2024] [Indexed: 05/26/2024]
Abstract
Computational chemistry is an indispensable tool for understanding molecules and predicting chemical properties. However, traditional computational methods face significant challenges due to the difficulty of solving the Schrödinger equations and the increasing computational cost with the size of the molecular system. In response, there has been a surge of interest in leveraging artificial intelligence (AI) and machine learning (ML) techniques to in silico experiments. Integrating AI and ML into computational chemistry increases the scalability and speed of the exploration of chemical space. However, challenges remain, particularly regarding the reproducibility and transferability of ML models. This review highlights the evolution of ML in learning from, complementing, or replacing traditional computational chemistry for energy and property predictions. Starting from models trained entirely on numerical data, a journey set forth toward the ideal model incorporating or learning the physical laws of quantum mechanics. This paper also reviews existing computational methods and ML models and their intertwining, outlines a roadmap for future research, and identifies areas for improvement and innovation. Ultimately, the goal is to develop AI architectures capable of predicting accurate and transferable solutions to the Schrödinger equation, thereby revolutionizing in silico experiments within chemistry and materials science.
Collapse
Affiliation(s)
- Abdulrahman Aldossary
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | | | - Sergio Pablo-García
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
| | - Shi Xuan Leong
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Ella Miray Rajaonson
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Luca Thiede
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Gary Tom
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
| | - Andrew Wang
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
| | - Davide Avagliano
- Chimie ParisTech, PSL University, CNRS, Institute of Chemistry for Life and Health Sciences (iCLeHS UMR 8060), Paris, F-75005, France
| | - Alán Aspuru-Guzik
- Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, ON, M5S 3H6, Canada
- Department of Computer Science, University of Toronto, 40 St. George Street, Toronto, ON, M5S 2E4, Canada
- Vector Institute for Artificial Intelligence, 661 University Ave. Suite 710, Toronto, ON, M5G 1M1, Canada
- Department of Materials Science & Engineering, University of Toronto, 184 College St., Toronto, ON, M5S 3E4, Canada
- Department of Chemical Engineering & Applied Chemistry, University of Toronto, 200 College St., Toronto, ON, M5S 3E5, Canada
- Lebovic Fellow, Canadian Institute for Advanced Research (CIFAR), 66118 University Ave., Toronto, M5G 1M1, Canada
- Acceleration Consortium, 80 St George St, Toronto, M5S 3H6, Canada
| |
Collapse
|
8
|
Radamson HH, Miao Y, Zhou Z, Wu Z, Kong Z, Gao J, Yang H, Ren Y, Zhang Y, Shi J, Xiang J, Cui H, Lu B, Li J, Liu J, Lin H, Xu H, Li M, Cao J, He C, Duan X, Zhao X, Su J, Du Y, Yu J, Wu Y, Jiang M, Liang D, Li B, Dong Y, Wang G. CMOS Scaling for the 5 nm Node and Beyond: Device, Process and Technology. NANOMATERIALS (BASEL, SWITZERLAND) 2024; 14:837. [PMID: 38786792 PMCID: PMC11123950 DOI: 10.3390/nano14100837] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Revised: 04/24/2024] [Accepted: 04/29/2024] [Indexed: 05/25/2024]
Abstract
After more than five decades, Moore's Law for transistors is approaching the end of the international technology roadmap of semiconductors (ITRS). The fate of complementary metal oxide semiconductor (CMOS) architecture has become increasingly unknown. In this era, 3D transistors in the form of gate-all-around (GAA) transistors are being considered as an excellent solution to scaling down beyond the 5 nm technology node, which solves the difficulties of carrier transport in the channel region which are mainly rooted in short channel effects (SCEs). In parallel to Moore, during the last two decades, transistors with a fully depleted SOI (FDSOI) design have also been processed for low-power electronics. Among all the possible designs, there are also tunneling field-effect transistors (TFETs), which offer very low power consumption and decent electrical characteristics. This review article presents new transistor designs, along with the integration of electronics and photonics, simulation methods, and continuation of CMOS process technology to the 5 nm technology node and beyond. The content highlights the innovative methods, challenges, and difficulties in device processing and design, as well as how to apply suitable metrology techniques as a tool to find out the imperfections and lattice distortions, strain status, and composition in the device structures.
Collapse
Affiliation(s)
- Henry H. Radamson
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Yuanhao Miao
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Ziwei Zhou
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Zhenhua Wu
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Zhenzhen Kong
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Jianfeng Gao
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Hong Yang
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Yuhui Ren
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Yongkui Zhang
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Jiangliu Shi
- Beijing Superstring Academy of Memory Technology, Beijing 100176, China; (J.S.); (J.X.); (M.J.); (D.L.)
| | - Jinjuan Xiang
- Beijing Superstring Academy of Memory Technology, Beijing 100176, China; (J.S.); (J.X.); (M.J.); (D.L.)
| | - Hushan Cui
- Jiangsu Leuven Instruments Co., Ltd., Xuzhou 221300, China;
| | - Bin Lu
- School of Physics and Information Engineering, Shanxi Normal University, Linfen 041004, China;
| | - Junjie Li
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Jinbiao Liu
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Hongxiao Lin
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Haoqing Xu
- Institute of Microelectronics, University of Chinese Academy of Sciences, Beijing 100049, China;
| | - Mengfan Li
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
- Institute of Microelectronics, University of Chinese Academy of Sciences, Beijing 100049, China;
| | - Jiaji Cao
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Chuangqi He
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Xiangyan Duan
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Xuewei Zhao
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
- Institute of Microelectronics, University of Chinese Academy of Sciences, Beijing 100049, China;
| | - Jiale Su
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Yong Du
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Jiahan Yu
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Yuanyuan Wu
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Miao Jiang
- Beijing Superstring Academy of Memory Technology, Beijing 100176, China; (J.S.); (J.X.); (M.J.); (D.L.)
| | - Di Liang
- Beijing Superstring Academy of Memory Technology, Beijing 100176, China; (J.S.); (J.X.); (M.J.); (D.L.)
| | - Ben Li
- Research and Development Center of Optoelectronic Hybrid IC, Guangdong Greater Bay Area Institute of Integrated Circuit and System, Guangzhou 510535, China; (Z.Z.); (Y.R.); (H.L.); (J.C.); (C.H.); (X.D.); (Y.W.); (B.L.)
| | - Yan Dong
- Key Laboratory of Microelectronics Devices & Integrated Technology, Institute of Microelectronics, Chinese Academy of Sciences, Beijing 100029, China; (Z.W.); (Z.K.); (J.G.); (H.Y.); (Y.Z.); (J.L.); (J.L.); (M.L.); (X.Z.); (J.S.); (Y.D.); (J.Y.); (Y.D.)
| | - Guilei Wang
- Beijing Superstring Academy of Memory Technology, Beijing 100176, China; (J.S.); (J.X.); (M.J.); (D.L.)
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| |
Collapse
|
9
|
Li X, Qian Y, Chen J. Electric Polarization from a Many-Body Neural Network Ansatz. PHYSICAL REVIEW LETTERS 2024; 132:176401. [PMID: 38728714 DOI: 10.1103/physrevlett.132.176401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2023] [Revised: 12/01/2023] [Accepted: 03/22/2024] [Indexed: 05/12/2024]
Abstract
Ab initio calculation of dielectric response with high-accuracy electronic structure methods is a long-standing problem, for which mean-field approaches are widely used and electron correlations are mostly treated via approximated functionals. Here we employ a neural network wave function ansatz combined with quantum Monte Carlo method to incorporate correlations into polarization calculations. On a variety of systems, including isolated atoms, one-dimensional chains, two-dimensional slabs, and three-dimensional cubes, the calculated results outperform conventional density functional theory and are consistent with the most accurate calculations and experimental data. Furthermore, we have studied the out-of-plane dielectric constant of bilayer graphene using our method and reestablished its thickness dependence. Overall, this approach provides a powerful tool to accurately describe electron correlation in the modern theory of polarization.
Collapse
Affiliation(s)
- Xiang Li
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Yubing Qian
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
- School of Physics, Peking University, Beijing 100871, People's Republic of China
| | - Ji Chen
- School of Physics, Peking University, Beijing 100871, People's Republic of China
- Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, Beijing 100871, People's Republic of China
| |
Collapse
|
10
|
Unke OT, Stöhr M, Ganscha S, Unterthiner T, Maennel H, Kashubin S, Ahlin D, Gastegger M, Medrano Sandonas L, Berryman JT, Tkatchenko A, Müller KR. Biomolecular dynamics with machine-learned quantum-mechanical force fields trained on diverse chemical fragments. SCIENCE ADVANCES 2024; 10:eadn4397. [PMID: 38579003 DOI: 10.1126/sciadv.adn4397] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/10/2023] [Accepted: 02/29/2024] [Indexed: 04/07/2024]
Abstract
The GEMS method enables molecular dynamics simulations of large heterogeneous systems at ab initio quality.
Collapse
Affiliation(s)
- Oliver T Unke
- Google DeepMind, Tucholskystraße 2, 10117 Berlin, Germany and Brandschenkestrasse 110, 8002 Zürich, Switzerland
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- DFG Cluster of Excellence "Unifying Systems in Catalysis" (UniSysCat), Technische Universität Berlin, 10623 Berlin, Germany
| | - Martin Stöhr
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Stefan Ganscha
- Google DeepMind, Tucholskystraße 2, 10117 Berlin, Germany and Brandschenkestrasse 110, 8002 Zürich, Switzerland
| | - Thomas Unterthiner
- Google DeepMind, Tucholskystraße 2, 10117 Berlin, Germany and Brandschenkestrasse 110, 8002 Zürich, Switzerland
| | - Hartmut Maennel
- Google DeepMind, Tucholskystraße 2, 10117 Berlin, Germany and Brandschenkestrasse 110, 8002 Zürich, Switzerland
| | - Sergii Kashubin
- Google DeepMind, Tucholskystraße 2, 10117 Berlin, Germany and Brandschenkestrasse 110, 8002 Zürich, Switzerland
| | - Daniel Ahlin
- Google DeepMind, Tucholskystraße 2, 10117 Berlin, Germany and Brandschenkestrasse 110, 8002 Zürich, Switzerland
| | - Michael Gastegger
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- DFG Cluster of Excellence "Unifying Systems in Catalysis" (UniSysCat), Technische Universität Berlin, 10623 Berlin, Germany
- BASLEARN - TU Berlin/BASF Joint Lab for Machine Learning, Technische Universität Berlin, 10587 Berlin, Germany
| | - Leonardo Medrano Sandonas
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Joshua T Berryman
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Klaus-Robert Müller
- Google DeepMind, Tucholskystraße 2, 10117 Berlin, Germany and Brandschenkestrasse 110, 8002 Zürich, Switzerland
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
- Department of Artificial Intelligence, Korea University, Anam-dong, Seongbuk-gu, Seoul 02841, Korea
- Max Planck Institute for Informatics, Stuhlsatzenhausweg, 66123 Saarbrücken, Germany
- BIFOLD - Berlin Institute for the Foundations of Learning and Data, Berlin, Germany
| |
Collapse
|
11
|
Zhang J, Benavides-Riveros CL, Chen L. Artificial-Intelligence-Based Surrogate Solution of Dissipative Quantum Dynamics: Physics-Informed Reconstruction of the Universal Propagator. J Phys Chem Lett 2024; 15:3603-3610. [PMID: 38527271 DOI: 10.1021/acs.jpclett.4c00598] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/27/2024]
Abstract
The accurate (or even approximate) solution of the equations that govern the dynamics of dissipative quantum systems remains a challenging task in quantum science. While several algorithms have been designed to solve those equations with different degrees of flexibility, they rely mainly on highly expensive iterative schemes. Most recently, deep neural networks have been used for quantum dynamics, but current architectures are highly dependent on the physics of the particular system and usually limited to population dynamics. Here we introduce an artificial-intelligence-based surrogate model that solves dissipative quantum dynamics by parametrizing quantum propagators as Fourier neural operators, which we train using both data set and physics-informed loss functions. Compared with conventional algorithms, our quantum neural propagator avoids time-consuming iterations and provides a universal superoperator that can be used to evolve any initial quantum state for arbitrarily long times. To illustrate the wide applicability of the approach, we employ our quantum neural propagator to compute the population dynamics and time-correlation functions of the Fenna-Matthews-Olson complex.
Collapse
|
12
|
Liu S. Harvesting Chemical Understanding with Machine Learning and Quantum Computers. ACS PHYSICAL CHEMISTRY AU 2024; 4:135-142. [PMID: 38560751 PMCID: PMC10979482 DOI: 10.1021/acsphyschemau.3c00067] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 12/06/2023] [Revised: 12/29/2023] [Accepted: 01/02/2024] [Indexed: 04/04/2024]
Abstract
It is tenable to argue that nobody can predict the future with certainty, yet one can learn from the past and make informed projections for the years ahead. In this Perspective, we overview the status of how theory and computation can be exploited to obtain chemical understanding from wave function theory and density functional theory, and then outlook the likely impact of machine learning (ML) and quantum computers (QC) to appreciate traditional chemical concepts in decades to come. It is maintained that the development and maturation of ML and QC methods in theoretical and computational chemistry represent two paradigm shifts about how the Schrödinger equation can be solved. New chemical understanding can be harnessed in these two new paradigms by making respective use of ML features and QC qubits. Before that happens, however, we still have hurdles to face and obstacles to overcome in both ML and QC arenas. Possible pathways to tackle these challenges are proposed. We anticipate that hierarchical modeling, in contrast to multiscale modeling, will emerge and thrive, becoming the workhorse of in silico simulations in the next few decades.
Collapse
|
13
|
Halder S, Dey A, Shrikhande C, Maitra R. Machine learning assisted construction of a shallow depth dynamic ansatz for noisy quantum hardware. Chem Sci 2024; 15:3279-3289. [PMID: 38425512 PMCID: PMC10901498 DOI: 10.1039/d3sc05807g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Accepted: 01/16/2024] [Indexed: 03/02/2024] Open
Abstract
The development of various dynamic ansatz-constructing techniques has ushered in a new era, making the practical exploitation of Noisy Intermediate-Scale Quantum (NISQ) hardware for molecular simulations increasingly viable. However, such ansatz construction protocols incur substantial measurement costs during their execution. This work involves the development of a novel protocol that capitalizes on regenerative machine learning methodologies and many-body perturbation theoretical measures to construct a highly expressive and shallow ansatz within the variational quantum eigensolver (VQE) framework with limited measurement costs. The regenerative machine learning model used in our work is trained with the basis vectors of a low-rank expansion of the N-electron Hilbert space to identify the dominant high-rank excited determinants without requiring a large number of quantum measurements. These selected excited determinants are iteratively incorporated within the ansatz through their low-rank decomposition. The reduction in the number of quantum measurements and ansatz depth manifests in the robustness of our method towards hardware noise, as demonstrated through numerical applications. Furthermore, the proposed method is highly compatible with state-of-the-art neural error mitigation techniques. This resource-efficient approach is quintessential for determining spectroscopic and other molecular properties, thereby facilitating the study of emerging chemical phenomena in the near-term quantum computing framework.
Collapse
Affiliation(s)
- Sonaldeep Halder
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Anish Dey
- Department of Chemical Sciences, Indian Institute of Science Education and Research Kolkata West Bengal 741246 India
| | - Chinmay Shrikhande
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| | - Rahul Maitra
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
| |
Collapse
|
14
|
Gashmard H, Shakeripour H, Alaei M. Predicting superconducting transition temperature through advanced machine learning and innovative feature engineering. Sci Rep 2024; 14:3965. [PMID: 38368476 PMCID: PMC10874381 DOI: 10.1038/s41598-024-54440-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2023] [Accepted: 02/13/2024] [Indexed: 02/19/2024] Open
Abstract
Superconductivity is a remarkable phenomenon in condensed matter physics, which comprises a fascinating array of properties expected to revolutionize energy-related technologies and pertinent fundamental research. However, the field faces the challenge of achieving superconductivity at room temperature. In recent years, Artificial Intelligence (AI) approaches have emerged as a promising tool for predicting such properties as transition temperature (Tc) to enable the rapid screening of large databases to discover new superconducting materials. This study employs the SuperCon dataset as the largest superconducting materials dataset. Then, we perform various data pre-processing steps to derive the clean DataG dataset, containing 13,022 compounds. In another stage of the study, we apply the novel CatBoost algorithm to predict the transition temperatures of novel superconducting materials. In addition, we developed a package called Jabir, which generates 322 atomic descriptors. We also designed an innovative hybrid method called the Soraya package to select the most critical features from the feature space. These yield R2 and RMSE values (0.952 and 6.45 K, respectively) superior to those previously reported in the literature. Finally, as a novel contribution to the field, a web application was designed for predicting and determining the Tc values of superconducting materials.
Collapse
Affiliation(s)
- Hassan Gashmard
- Department of Physics, Isfahan University of Technology, Isfahan, 84156-83111, Iran
| | - Hamideh Shakeripour
- Department of Physics, Isfahan University of Technology, Isfahan, 84156-83111, Iran.
| | - Mojtaba Alaei
- Department of Physics, Isfahan University of Technology, Isfahan, 84156-83111, Iran
| |
Collapse
|
15
|
Xi B, Chan MK, Bao K, Zhao W, Chan HM, Chen H, Zhu J. Parameter-Free and Electron Counting Satisfied Material Representation for Machine Learning Potential Energy and Force Fields. J Phys Chem Lett 2024; 15:1636-1643. [PMID: 38306617 PMCID: PMC10875669 DOI: 10.1021/acs.jpclett.3c03250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/18/2023] [Revised: 01/28/2024] [Accepted: 01/29/2024] [Indexed: 02/04/2024]
Abstract
We proposed a parameter-free volume element representation that satisfies the electron counting model and obtains accurate machine learning potential energy and direct force fitting of randomly perturbed hexagonal BN. Our method preserves permutational, translational, and rotational invariance and can be extended to three-dimensional systems, verified by a system of bulk Si. As a result, we obtained 0.57 meV/atom potential energy root mean squared error (RMSE) and 59 meV/Å force RMSE for perturbed bulk BN systems and 0.43 meV/atom potential energy RMSE and 36 meV/Å force RMSE for perturbed Si systems. In addition, an unbiased perturbation-based data set construction scheme is introduced and a continuous population distribution is obtained with a training data set of 4500, which is about 1 order of magnitude smaller than standard methods based on first-principles molecular dynamics simulations and saves a large amount of computing resources. General validity of our model is verified by structure optimization, molecular dynamics simulations, and extrapolations.
Collapse
Affiliation(s)
- Bin Xi
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Man Kit Chan
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Kejie Bao
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Wenjing Zhao
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Ho Ming Chan
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Hang Chen
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| | - Junyi Zhu
- Department of Physics, The Chinese University of Hong Kong, Shatin, New Territory, Hong Kong SAR 999077, P.R. China
| |
Collapse
|
16
|
Nicolle A, Deng S, Ihme M, Kuzhagaliyeva N, Ibrahim EA, Farooq A. Mixtures Recomposition by Neural Nets: A Multidisciplinary Overview. J Chem Inf Model 2024; 64:597-620. [PMID: 38284618 DOI: 10.1021/acs.jcim.3c01633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2024]
Abstract
Artificial Neural Networks (ANNs) are transforming how we understand chemical mixtures, providing an expressive view of the chemical space and multiscale processes. Their hybridization with physical knowledge can bridge the gap between predictivity and understanding of the underlying processes. This overview explores recent progress in ANNs, particularly their potential in the 'recomposition' of chemical mixtures. Graph-based representations reveal patterns among mixture components, and deep learning models excel in capturing complexity and symmetries when compared to traditional Quantitative Structure-Property Relationship models. Key components, such as Hamiltonian networks and convolution operations, play a central role in representing multiscale mixtures. The integration of ANNs with Chemical Reaction Networks and Physics-Informed Neural Networks for inverse chemical kinetic problems is also examined. The combination of sensors with ANNs shows promise in optical and biomimetic applications. A common ground is identified in the context of statistical physics, where ANN-based methods iteratively adapt their models by blending their initial states with training data. The concept of mixture recomposition unveils a reciprocal inspiration between ANNs and reactive mixtures, highlighting learning behaviors influenced by the training environment.
Collapse
Affiliation(s)
- Andre Nicolle
- Aramco Fuel Research Center, Rueil-Malmaison 92852, France
| | - Sili Deng
- Massachusetts Institute of Technology, Cambridge 02139, Massachusetts, United States
| | - Matthias Ihme
- Stanford University, Stanford 94305, California, United States
| | | | - Emad Al Ibrahim
- King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
| | - Aamir Farooq
- King Abdullah University of Science and Technology, Thuwal 23955, Saudi Arabia
| |
Collapse
|
17
|
Griffin C, Karn T, Apple B. Topological learning in multiclass data sets. Phys Rev E 2024; 109:024131. [PMID: 38491638 DOI: 10.1103/physreve.109.024131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/23/2023] [Accepted: 02/01/2024] [Indexed: 03/18/2024]
Abstract
We specialize techniques from topological data analysis to the problem of characterizing the topological complexity (as defined in the body of the paper) of a multiclass data set. As a by-product, a topological classifier is defined that uses an open subcovering of the data set. This subcovering can be used to construct a simplicial complex whose topological features (e.g., Betti numbers) provide information about the classification problem. We use these topological constructs to study the impact of topological complexity on learning in feedforward deep neural networks (DNNs). We hypothesize that topological complexity is negatively correlated with the ability of a fully connected feedforward deep neural network to learn to classify data correctly. We evaluate our topological classification algorithm on multiple constructed and open-source data sets. We also validate our hypothesis regarding the relationship between topological complexity and learning in DNN's on multiple data sets.
Collapse
Affiliation(s)
- Christopher Griffin
- Applied Research Laboratory, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
| | - Trevor Karn
- School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Benjamin Apple
- Naval Surface Warfare Center Carderock, Bethesda Maryland 20817, USA
| |
Collapse
|
18
|
Scherbela M, Gerard L, Grohs P. Towards a transferable fermionic neural wavefunction for molecules. Nat Commun 2024; 15:120. [PMID: 38168035 PMCID: PMC10762074 DOI: 10.1038/s41467-023-44216-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2023] [Accepted: 12/05/2023] [Indexed: 01/05/2024] Open
Abstract
Deep neural networks have become a highly accurate and powerful wavefunction ansatz in combination with variational Monte Carlo methods for solving the electronic Schrödinger equation. However, despite their success and favorable scaling, these methods are still computationally too costly for wide adoption. A significant obstacle is the requirement to optimize the wavefunction from scratch for each new system, thus requiring long optimization. In this work, we propose a neural network ansatz, which effectively maps uncorrelated, computationally cheap Hartree-Fock orbitals, to correlated, high-accuracy neural network orbitals. This ansatz is inherently capable of learning a single wavefunction across multiple compounds and geometries, as we demonstrate by successfully transferring a wavefunction model pre-trained on smaller fragments to larger compounds. Furthermore, we provide ample experimental evidence to support the idea that extensive pre-training of such a generalized wavefunction model across different compounds and geometries could lead to a foundation wavefunction model. Such a model could yield high-accuracy ab-initio energies using only minimal computational effort for fine-tuning and evaluation of observables.
Collapse
Affiliation(s)
| | - Leon Gerard
- Research Network Data Science, University of Vienna, Vienna, Austria
| | - Philipp Grohs
- Faculty of Mathematics, University of Vienna, Vienna, Austria.
- Research Network Data Science, University of Vienna, Vienna, Austria.
- Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences, Linz, Austria.
| |
Collapse
|
19
|
Ditte M, Barborini M, Medrano Sandonas L, Tkatchenko A. Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators. PHYSICAL REVIEW LETTERS 2023; 131:228001. [PMID: 38101380 DOI: 10.1103/physrevlett.131.228001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/29/2023] [Revised: 07/26/2023] [Accepted: 10/20/2023] [Indexed: 12/17/2023]
Abstract
We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.
Collapse
Affiliation(s)
- Matej Ditte
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Matteo Barborini
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Leonardo Medrano Sandonas
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg City, Luxembourg
| |
Collapse
|
20
|
Li X, Huang JC, Zhang GZ, Li HE, Cao CS, Lv D, Hu HS. A Nonstochastic Optimization Algorithm for Neural-Network Quantum States. J Chem Theory Comput 2023; 19:8156-8165. [PMID: 37962975 DOI: 10.1021/acs.jctc.3c00831] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2023]
Abstract
Neural-network quantum states (NQS) employ artificial neural networks to encode many-body wave functions in a second quantization through variational Monte Carlo (VMC). They have recently been applied to accurately describe electronic wave functions of molecules and have shown the challenges in efficiency compared with traditional quantum chemistry methods. Here, we introduce a general nonstochastic optimization algorithm for NQS in chemical systems, which deterministically generates a selected set of important configurations simultaneously with energy evaluation of NQS. This method bypasses the need for Markov-chain Monte Carlo within the VMC framework, thereby accelerating the entire optimization process. Furthermore, this newly developed nonstochastic optimization algorithm for NQS offers comparable or superior accuracy compared to its stochastic counterpart and ensures more stable convergence. The application of this model to test molecules exhibiting strong electron correlations provides further insight into the performance of NQS in chemical systems and opens avenues for future enhancements.
Collapse
Affiliation(s)
- Xiang Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Jia-Cheng Huang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Guang-Ze Zhang
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Hao-En Li
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| | - Chang-Su Cao
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
- ByteDance Research, Zhonghang Plaza, No. 43, North Third Ring West Road, Haidian District, Beijing 100089, China
| | - Dingshun Lv
- ByteDance Research, Zhonghang Plaza, No. 43, North Third Ring West Road, Haidian District, Beijing 100089, China
| | - Han-Shi Hu
- Department of Chemistry and Engineering Research Center of Advanced Rare-Earth Materials of Ministry of Education, Tsinghua University, Beijing 100084, China
| |
Collapse
|
21
|
Mazo-Sevillano PD, Hermann J. Variational principle to regularize machine-learned density functionals: The non-interacting kinetic-energy functional. J Chem Phys 2023; 159:194107. [PMID: 37971033 DOI: 10.1063/5.0166432] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2023] [Accepted: 10/26/2023] [Indexed: 11/19/2023] Open
Abstract
Practical density functional theory (DFT) owes its success to the groundbreaking work of Kohn and Sham that introduced the exact calculation of the non-interacting kinetic energy of the electrons using an auxiliary mean-field system. However, the full power of DFT will not be unleashed until the exact relationship between the electron density and the non-interacting kinetic energy is found. Various attempts have been made to approximate this functional, similar to the exchange-correlation functional, with much less success due to the larger contribution of kinetic energy and its more non-local nature. In this work, we propose a new and efficient regularization method to train density functionals based on deep neural networks, with particular interest in the kinetic-energy functional. The method is tested on (effectively) one-dimensional systems, including the hydrogen chain, non-interacting electrons, and atoms of the first two periods, with excellent results. For atomic systems, the generalizability of the regularization method is demonstrated by training also an exchange-correlation functional, and the contrasting nature of the two functionals is discussed from a machine-learning perspective.
Collapse
Affiliation(s)
- Pablo Del Mazo-Sevillano
- Departamento de Química Física Aplicada, Universidad Autónoma de Madrid, Módulo 14, 28049 Madrid, Spain
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Jan Hermann
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195 Berlin, Germany
- Microsoft Research AI4Science, Karl-Liebknecht-Str. 32, 10178 Berlin, Germany
| |
Collapse
|
22
|
Nomura Y. Boltzmann machines and quantum many-body problems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2023; 36:073001. [PMID: 37918107 DOI: 10.1088/1361-648x/ad0916] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/02/2023] [Accepted: 11/02/2023] [Indexed: 11/04/2023]
Abstract
Analyzing quantum many-body problems and elucidating the entangled structure of quantum states is a significant challenge common to a wide range of fields. Recently, a novel approach using machine learning was introduced to address this challenge. The idea is to 'embed' nontrivial quantum correlations (quantum entanglement) into artificial neural networks. Through intensive developments, artificial neural network methods are becoming new powerful tools for analyzing quantum many-body problems. Among various artificial neural networks, this topical review focuses on Boltzmann machines and provides an overview of recent developments and applications.
Collapse
Affiliation(s)
- Yusuke Nomura
- Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama 223-8522, Japan
| |
Collapse
|
23
|
Dey M, Ghosh D. Machine Learning the Quantum Mechanical Wave Function. J Phys Chem A 2023; 127:9159-9166. [PMID: 37906959 DOI: 10.1021/acs.jpca.3c05322] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2023]
Abstract
Strongly correlated systems have been challenging to computational chemists for a long time. To solve these systems, multireference methods have been developed over the years. Recently, with the fast development of machine learning and artificial intelligence methods, these methods have also influenced the quest for optimal wave function ansatz. Machine learning approaches have been used in many different flavors. From this perspective, we will discuss the different milestones achieved in the use of machine learning for solving the quantum many body problem.
Collapse
Affiliation(s)
- Mandira Dey
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| | - Debashree Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India
| |
Collapse
|
24
|
Huguenin-Dumittan K, Loche P, Haoran N, Ceriotti M. Physics-Inspired Equivariant Descriptors of Nonbonded Interactions. J Phys Chem Lett 2023; 14:9612-9618. [PMID: 37862712 PMCID: PMC10626632 DOI: 10.1021/acs.jpclett.3c02375] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2023] [Accepted: 10/13/2023] [Indexed: 10/22/2023]
Abstract
One essential ingredient in many machine learning (ML) based methods for atomistic modeling of materials and molecules is the use of locality. While allowing better system-size scaling, this systematically neglects long-range (LR) effects such as electrostatic or dispersion interactions. We present an extension of the long distance equivariant (LODE) framework that can handle diverse LR interactions in a consistent way and seamlessly integrates with preexisting methods by building new sets of atom centered features. We provide a direct physical interpretation of these using the multipole expansion, which allows for simpler and more efficient implementations. The framework is applied to simple toy systems as proof of concept and a heterogeneous set of molecular dimers to push the method to its limits. By generalizing LODE to arbitrary asymptotic behaviors, we provide a coherent approach to treat arbitrary two- and many-body nonbonded interactions in the data-driven modeling of matter.
Collapse
Affiliation(s)
- Kevin
K. Huguenin-Dumittan
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Philip Loche
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Ni Haoran
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Michele Ceriotti
- Laboratory
of Computational Science and Modeling, IMX,
École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| |
Collapse
|
25
|
Shao X, Paetow L, Tuckerman ME, Pavanello M. Machine learning electronic structure methods based on the one-electron reduced density matrix. Nat Commun 2023; 14:6281. [PMID: 37805614 PMCID: PMC10560258 DOI: 10.1038/s41467-023-41953-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Accepted: 09/18/2023] [Indexed: 10/09/2023] Open
Abstract
The theorems of density functional theory (DFT) establish bijective maps between the local external potential of a many-body system and its electron density, wavefunction and, therefore, one-particle reduced density matrix. Building on this foundation, we show that machine learning models based on the one-electron reduced density matrix can be used to generate surrogate electronic structure methods. We generate surrogates of local and hybrid DFT, Hartree-Fock and full configuration interaction theories for systems ranging from small molecules such as water to more complex compounds like benzene and propanol. The surrogate models use the one-electron reduced density matrix as the central quantity to be learned. From the predicted density matrices, we show that either standard quantum chemistry or a second machine-learning model can be used to compute molecular observables, energies, and atomic forces. The surrogate models can generate essentially anything that a standard electronic structure method can, ranging from band gaps and Kohn-Sham orbitals to energy-conserving ab-initio molecular dynamics simulations and infrared spectra, which account for anharmonicity and thermal effects, without the need to employ computationally expensive algorithms such as self-consistent field theory. The algorithms are packaged in an efficient and easy to use Python code, QMLearn, accessible on popular platforms.
Collapse
Affiliation(s)
- Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, NJ, 07102, USA.
| | - Lukas Paetow
- Department of Chemistry, Rutgers University, Newark, NJ, 07102, USA
| | - Mark E Tuckerman
- Department of Chemistry, New York University, New York, NY, 10003, USA.
- Courant Institute of Mathematical Science, New York University, New York, NY, 10003, USA.
- Simons Center for Computational Physical Chemistry, New York University, New York, NY, 10003, USA.
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, 200062, Shanghai, China.
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, NJ, 07102, USA.
- Department of Physics, Rutgers University, Newark, NJ, 07102, USA.
| |
Collapse
|
26
|
Hermann J, Spencer J, Choo K, Mezzacapo A, Foulkes WMC, Pfau D, Carleo G, Noé F. Ab initio quantum chemistry with neural-network wavefunctions. Nat Rev Chem 2023; 7:692-709. [PMID: 37558761 DOI: 10.1038/s41570-023-00516-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 06/16/2023] [Indexed: 08/11/2023]
Abstract
Deep learning methods outperform human capabilities in pattern recognition and data processing problems and now have an increasingly important role in scientific discovery. A key application of machine learning in molecular science is to learn potential energy surfaces or force fields from ab initio solutions of the electronic Schrödinger equation using data sets obtained with density functional theory, coupled cluster or other quantum chemistry (QC) methods. In this Review, we discuss a complementary approach using machine learning to aid the direct solution of QC problems from first principles. Specifically, we focus on quantum Monte Carlo methods that use neural-network ansatzes to solve the electronic Schrödinger equation, in first and second quantization, computing ground and excited states and generalizing over multiple nuclear configurations. Although still at their infancy, these methods can already generate virtually exact solutions of the electronic Schrödinger equation for small systems and rival advanced conventional QC methods for systems with up to a few dozen electrons.
Collapse
Affiliation(s)
- Jan Hermann
- Microsoft Research AI4Science, Berlin, Germany
- FU Berlin, Department of Mathematics and Computer Science, Berlin, Germany
| | | | - Kenny Choo
- Department of Physics, University of Zurich, Zurich, Switzerland
- IBM Quantum, IBM Research Zurich, Ruschlikon, Switzerland
| | | | - W M C Foulkes
- Imperial College London, Department of Physics, London, UK
| | - David Pfau
- DeepMind, London, UK.
- Imperial College London, Department of Physics, London, UK.
| | | | - Frank Noé
- Microsoft Research AI4Science, Berlin, Germany.
- FU Berlin, Department of Mathematics and Computer Science, Berlin, Germany.
- FU Berlin, Department of Physics, Berlin, Germany.
- Department of Chemistry,Rice University, Houston, TX, USA.
| |
Collapse
|
27
|
Joung S, Ghim YC, Kim J, Kwak S, Kwon D, Sung C, Kim D, Kim HS, Bak JG, Yoon SW. GS-DeepNet: mastering tokamak plasma equilibria with deep neural networks and the Grad-Shafranov equation. Sci Rep 2023; 13:15799. [PMID: 37737481 PMCID: PMC10516960 DOI: 10.1038/s41598-023-42991-5] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2023] [Accepted: 09/18/2023] [Indexed: 09/23/2023] Open
Abstract
The force-balanced state of magnetically confined plasmas heated up to 100 million degrees Celsius must be sustained long enough to achieve a burning-plasma state, such as in the case of ITER, a fusion reactor that promises a net energy gain. This force balance between the Lorentz force and the pressure gradient force, known as a plasma equilibrium, can be theoretically portrayed together with Maxwell's equations as plasmas are collections of charged particles. Nevertheless, identifying the plasma equilibrium in real time is challenging owing to its free-boundary and ill-posed conditions, which conventionally involves iterative numerical approach with a certain degree of subjective human decisions such as including or excluding certain magnetic measurements to achieve numerical convergence on the solution as well as to avoid unphysical solutions. Here, we introduce GS-DeepNet, which learns plasma equilibria through solely unsupervised learning, without using traditional numerical algorithms. GS-DeepNet includes two neural networks and teaches itself. One neural network generates a possible candidate of an equilibrium following Maxwell's equations and is taught by the other network satisfying the force balance under the equilibrium. Measurements constrain both networks. Our GS-DeepNet achieves reliable equilibria with uncertainties in contrast with existing methods, leading to possible better control of fusion-grade plasmas.
Collapse
Affiliation(s)
- Semin Joung
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon, 34141, South Korea.
- University of Wisconsin-Madison, Madison, WI, 53706, USA.
| | - Y-C Ghim
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon, 34141, South Korea.
| | - Jaewook Kim
- Korea Institute of Fusion Energy, Daejeon, 34133, South Korea
| | - Sehyun Kwak
- Max-Planck-Institute Fur Plasmaphysik, 17491, Greifswald, Germany
| | - Daeho Kwon
- Mobiis Co., Ltd., Seongnam-Si, Gyeonggi-Do, 13486, South Korea
| | - C Sung
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon, 34141, South Korea
| | - D Kim
- Department of Nuclear and Quantum Engineering, KAIST, Daejeon, 34141, South Korea
| | - Hyun-Seok Kim
- Korea Institute of Fusion Energy, Daejeon, 34133, South Korea
| | - J G Bak
- Korea Institute of Fusion Energy, Daejeon, 34133, South Korea
| | - S W Yoon
- Korea Institute of Fusion Energy, Daejeon, 34133, South Korea
| |
Collapse
|
28
|
Martyn JM, Najafi K, Luo D. Variational Neural-Network Ansatz for Continuum Quantum Field Theory. PHYSICAL REVIEW LETTERS 2023; 131:081601. [PMID: 37683171 DOI: 10.1103/physrevlett.131.081601] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 07/21/2023] [Accepted: 07/25/2023] [Indexed: 09/10/2023]
Abstract
Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state's Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.
Collapse
Affiliation(s)
- John M Martyn
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- The NSF AI Institute for Artificial Intelligence and Fundamental Interactions
| | - Khadijeh Najafi
- IBM Quantum, IBM T. J. Watson Research Center, Yorktown Heights, New York 10598, USA
- MIT-IBM Watson AI Lab, Cambridge, Massachusetts 02142, USA
| | - Di Luo
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- The NSF AI Institute for Artificial Intelligence and Fundamental Interactions
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| |
Collapse
|
29
|
Wang H, Fu T, Du Y, Gao W, Huang K, Liu Z, Chandak P, Liu S, Van Katwyk P, Deac A, Anandkumar A, Bergen K, Gomes CP, Ho S, Kohli P, Lasenby J, Leskovec J, Liu TY, Manrai A, Marks D, Ramsundar B, Song L, Sun J, Tang J, Veličković P, Welling M, Zhang L, Coley CW, Bengio Y, Zitnik M. Scientific discovery in the age of artificial intelligence. Nature 2023; 620:47-60. [PMID: 37532811 DOI: 10.1038/s41586-023-06221-2] [Citation(s) in RCA: 76] [Impact Index Per Article: 76.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 05/16/2023] [Indexed: 08/04/2023]
Abstract
Artificial intelligence (AI) is being increasingly integrated into scientific discovery to augment and accelerate research, helping scientists to generate hypotheses, design experiments, collect and interpret large datasets, and gain insights that might not have been possible using traditional scientific methods alone. Here we examine breakthroughs over the past decade that include self-supervised learning, which allows models to be trained on vast amounts of unlabelled data, and geometric deep learning, which leverages knowledge about the structure of scientific data to enhance model accuracy and efficiency. Generative AI methods can create designs, such as small-molecule drugs and proteins, by analysing diverse data modalities, including images and sequences. We discuss how these methods can help scientists throughout the scientific process and the central issues that remain despite such advances. Both developers and users of AI toolsneed a better understanding of when such approaches need improvement, and challenges posed by poor data quality and stewardship remain. These issues cut across scientific disciplines and require developing foundational algorithmic approaches that can contribute to scientific understanding or acquire it autonomously, making them critical areas of focus for AI innovation.
Collapse
Affiliation(s)
- Hanchen Wang
- Department of Engineering, University of Cambridge, Cambridge, UK
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA
- Department of Research and Early Development, Genentech Inc, South San Francisco, CA, USA
- Department of Computer Science, Stanford University, Stanford, CA, USA
| | - Tianfan Fu
- Department of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, USA
| | - Yuanqi Du
- Department of Computer Science, Cornell University, Ithaca, NY, USA
| | - Wenhao Gao
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Kexin Huang
- Department of Computer Science, Stanford University, Stanford, CA, USA
| | - Ziming Liu
- Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Payal Chandak
- Harvard-MIT Program in Health Sciences and Technology, Cambridge, MA, USA
| | - Shengchao Liu
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- Université de Montréal, Montreal, Quebec, Canada
| | - Peter Van Katwyk
- Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI, USA
- Data Science Institute, Brown University, Providence, RI, USA
| | - Andreea Deac
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- Université de Montréal, Montreal, Quebec, Canada
| | - Anima Anandkumar
- Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA
- NVIDIA, Santa Clara, CA, USA
| | - Karianne Bergen
- Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI, USA
- Data Science Institute, Brown University, Providence, RI, USA
| | - Carla P Gomes
- Department of Computer Science, Cornell University, Ithaca, NY, USA
| | - Shirley Ho
- Center for Computational Astrophysics, Flatiron Institute, New York, NY, USA
- Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA
- Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA
- Department of Physics and Center for Data Science, New York University, New York, NY, USA
| | | | - Joan Lasenby
- Department of Engineering, University of Cambridge, Cambridge, UK
| | - Jure Leskovec
- Department of Computer Science, Stanford University, Stanford, CA, USA
| | | | - Arjun Manrai
- Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA
| | - Debora Marks
- Department of Systems Biology, Harvard Medical School, Boston, MA, USA
- Broad Institute of MIT and Harvard, Cambridge, MA, USA
| | | | - Le Song
- BioMap, Beijing, China
- Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates
| | - Jimeng Sun
- University of Illinois at Urbana-Champaign, Champaign, IL, USA
| | - Jian Tang
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- HEC Montréal, Montreal, Quebec, Canada
- CIFAR AI Chair, Toronto, Ontario, Canada
| | - Petar Veličković
- Google DeepMind, London, UK
- Department of Computer Science and Technology, University of Cambridge, Cambridge, UK
| | - Max Welling
- University of Amsterdam, Amsterdam, Netherlands
- Microsoft Research Amsterdam, Amsterdam, Netherlands
| | - Linfeng Zhang
- DP Technology, Beijing, China
- AI for Science Institute, Beijing, China
| | - Connor W Coley
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Yoshua Bengio
- Mila - Quebec AI Institute, Montreal, Quebec, Canada
- Université de Montréal, Montreal, Quebec, Canada
| | - Marinka Zitnik
- Department of Biomedical Informatics, Harvard Medical School, Boston, MA, USA.
- Broad Institute of MIT and Harvard, Cambridge, MA, USA.
- Harvard Data Science Initiative, Cambridge, MA, USA.
- Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University, Cambridge, MA, USA.
| |
Collapse
|
30
|
Xiao P, Yun X, Chen Y, Guo X, Gao P, Zhou G, Zheng C. Insights into the solvation chemistry in liquid electrolytes for lithium-based rechargeable batteries. Chem Soc Rev 2023; 52:5255-5316. [PMID: 37462967 DOI: 10.1039/d3cs00151b] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/01/2023]
Abstract
Lithium-based rechargeable batteries have dominated the energy storage field and attracted considerable research interest due to their excellent electrochemical performance. As indispensable and ubiquitous components, electrolytes play a pivotal role in not only transporting lithium ions, but also expanding the electrochemical stable potential window, suppressing the side reactions, and manipulating the redox mechanism, all of which are closely associated with the behavior of solvation chemistry in electrolytes. Thus, comprehensively understanding the solvation chemistry in electrolytes is of significant importance. Here we critically reviewed the development of electrolytes in various lithium-based rechargeable batteries including lithium-metal batteries (LMBs), nonaqueous lithium-ion batteries (LIBs), lithium-sulfur batteries (LSBs), lithium-oxygen batteries (LOBs), and aqueous lithium-ion batteries (ALIBs), and emphasized the effects of interactions between cations, anions, and solvents on solvation chemistry, and functions of solvation chemistry in different types of electrolytes (strong solvating electrolytes, moderate solvating electrolytes, and weak solvating electrolytes) on the electrochemical performance and redox mechanism in the abovementioned rechargeable batteries. Specifically, the significant effects of solvation chemistry on the stability of electrode-electrolyte interphases, suppression of lithium dendrites in LMBs, inhibition of the co-intercalation of solvents in LIBs, improvement of anodic stability at high cut-off voltages in LMBs, LIBs and ALIBs, regulation of redox pathways in LSBs and LOBs, and inhibition of hydrogen/oxygen evolution reactions in LOBs are thoroughly summarized. Finally, the review concludes with a prospective outlook, where practical issues of electrolytes, advanced in situ/operando techniques to illustrate the mechanism of solvation chemistry, and advanced theoretical calculation and simulation techniques such as "material knowledge informed machine learning" and "artificial intelligence (AI) + big data" driven strategies for high-performance electrolytes have been proposed.
Collapse
Affiliation(s)
- Peitao Xiao
- College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China.
| | - Xiaoru Yun
- College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China.
| | - Yufang Chen
- College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China.
| | - Xiaowei Guo
- College of Computer, National University of Defense Technology, Changsha, Hunan, 410073, China
| | - Peng Gao
- College of Materials Science and Engineering, Hunan Joint International Laboratory of Advanced Materials and Technology of Clean Energy, Hunan Province Key Laboratory for Advanced Carbon Materials and Applied Technology, Hunan University Changsha, Changsha, Hunan, 410082, China
| | - Guangmin Zhou
- Tsinghua-Berkeley Shenzhen Institute & Tsinghua, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China.
| | - Chunman Zheng
- College of Aerospace Science and Engineering, National University of Defense Technology, Changsha, Hunan, 410073, China.
| |
Collapse
|
31
|
Huang B, von Rudorff GF, von Lilienfeld OA. The central role of density functional theory in the AI age. Science 2023; 381:170-175. [PMID: 37440654 DOI: 10.1126/science.abn3445] [Citation(s) in RCA: 13] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Accepted: 05/30/2023] [Indexed: 07/15/2023]
Abstract
Density functional theory (DFT) plays a pivotal role in chemical and materials science because of its relatively high predictive power, applicability, versatility, and computational efficiency. We review recent progress in machine learning (ML) model developments, which have relied heavily on DFT for synthetic data generation and for the design of model architectures. The general relevance of these developments is placed in a broader context for chemical and materials sciences. DFT-based ML models have reached high efficiency, accuracy, scalability, and transferability and pave the way to the routine use of successful experimental planning software within self-driving laboratories.
Collapse
Affiliation(s)
- Bing Huang
- University of Vienna, Faculty of Physics, AT1090 Wien, Austria
| | - Guido Falk von Rudorff
- University Kassel, Department of Chemistry, 34132 Kassel, Germany
- Center for Interdisciplinary Nanostructure Science and Technology (CINSaT), 34132 Kassel, Germany
| | - O Anatole von Lilienfeld
- Vector Institute for Artificial Intelligence, Toronto, Ontario M5S 1M1, Canada
- Department of Chemistry, University of Toronto, St. George Campus, Toronto, Ontario M5S 3H6, Canada
- Department of Materials Science and Engineering, University of Toronto, St. George Campus, Toronto, Ontario M5S 3E4, Canada
- Department of Physics, University of Toronto, St. George Campus, Toronto, Ontario M5S 1A7, Canada
- Machine Learning Group, Technische Universität Berlin and Berlin Institute for the Foundations of Learning and Data, 10587 Berlin, Germany
| |
Collapse
|
32
|
Jones GM, Li RR, DePrince AE, Vogiatzis KD. Data-Driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory. J Phys Chem Lett 2023:6377-6385. [PMID: 37418691 DOI: 10.1021/acs.jpclett.3c01382] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/09/2023]
Abstract
The exponential computational cost of describing strongly correlated electrons can be mitigated by adopting a reduced-density matrix (RDM)-based description of the electronic structure. While variational two-electron RDM (v2RDM) methods can enable large-scale calculations on such systems, the quality of the solution is limited by the fact that only a subset of known necessary N-representability constraints can be applied to the 2RDM in practical calculations. Here, we demonstrate that violations of partial three-particle (T1 and T2) N-representability conditions, which can be evaluated with knowledge of only the 2RDM, can serve as physics-based features in a machine-learning (ML) protocol for improving energies from v2RDM calculations that consider only two-particle (PQG) conditions. Proof-of-principle calculations demonstrate that the model yields substantially improved energies relative to reference values from configuration-interaction-based calculations.
Collapse
Affiliation(s)
- Grier M Jones
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
| | - Run R Li
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | - A Eugene DePrince
- Department of Chemistry and Biochemistry, Florida State University, Tallahassee, Florida 32306-4390, United States
| | | |
Collapse
|
33
|
Atanasova H, Bernheimer L, Cohen G. Stochastic representation of many-body quantum states. Nat Commun 2023; 14:3601. [PMID: 37328458 DOI: 10.1038/s41467-023-39244-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/16/2022] [Accepted: 06/02/2023] [Indexed: 06/18/2023] Open
Abstract
The quantum many-body problem is ultimately a curse of dimensionality: the state of a system with many particles is determined by a function with many dimensions, which rapidly becomes difficult to efficiently store, evaluate and manipulate numerically. On the other hand, modern machine learning models like deep neural networks can express highly correlated functions in extremely large-dimensional spaces, including those describing quantum mechanical problems. We show that if one represents wavefunctions as a stochastically generated set of sample points, the problem of finding ground states can be reduced to one where the most technically challenging step is that of performing regression-a standard supervised learning task. In the stochastic representation the (anti)symmetric property of fermionic/bosonic wavefunction can be used for data augmentation and learned rather than explicitly enforced. We further demonstrate that propagation of an ansatz towards the ground state can then be performed in a more robust and computationally scalable fashion than traditional variational approaches allow.
Collapse
Affiliation(s)
| | - Liam Bernheimer
- School of Chemistry, Tel Aviv University, Tel Aviv, 6997801, Israel
| | - Guy Cohen
- School of Chemistry, Tel Aviv University, Tel Aviv, 6997801, Israel.
- The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv, 6997801, Israel.
| |
Collapse
|
34
|
Haupt JP, Hosseini SM, López Ríos P, Dobrautz W, Cohen A, Alavi A. Optimizing Jastrow factors for the transcorrelated method. J Chem Phys 2023; 158:2895246. [PMID: 37290083 DOI: 10.1063/5.0147877] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Accepted: 05/25/2023] [Indexed: 06/10/2023] Open
Abstract
We investigate the optimization of flexible tailored real-space Jastrow factors for use in the transcorrelated (TC) method in combination with highly accurate quantum chemistry methods, such as initiator full configuration interaction quantum Monte Carlo (FCIQMC). Jastrow factors obtained by minimizing the variance of the TC reference energy are found to yield better, more consistent results than those obtained by minimizing the variational energy. We compute all-electron atomization energies for the challenging first-row molecules C2, CN, N2, and O2 and find that the TC method yields chemically accurate results using only the cc-pVTZ basis set, roughly matching the accuracy of non-TC calculations with the much larger cc-pV5Z basis set. We also investigate an approximation in which pure three-body excitations are neglected from the TC-FCIQMC dynamics, saving storage and computational costs, and show that it affects relative energies negligibly. Our results demonstrate that the combination of tailored real-space Jastrow factors with the multi-configurational TC-FCIQMC method provides a route to obtaining chemical accuracy using modest basis sets, obviating the need for basis-set extrapolation and composite techniques.
Collapse
Affiliation(s)
- J Philip Haupt
- Max-Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | | | - Pablo López Ríos
- Max-Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
| | - Werner Dobrautz
- Department of Chemistry and Chemical Engineering, Chalmers University of Technology, 41296 Gothenburg, Sweden
| | - Aron Cohen
- DeepMind, 6 Pancras Square, London N1C 4AG, United Kingdom
| | - Ali Alavi
- Max-Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| |
Collapse
|
35
|
Chen Y, Zhang L, E W, Car R. Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems. J Chem Theory Comput 2023. [PMID: 37071815 PMCID: PMC10373495 DOI: 10.1021/acs.jctc.3c00038] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/20/2023]
Abstract
We propose a quantum Monte Carlo approach to solve the many-body Schrödinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations dominated by either dynamic or static electronic correlation.
Collapse
Affiliation(s)
- Yixiao Chen
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, United States
| | - Linfeng Zhang
- AI for Science Institute, Beijing 100080, People's Republic of China
- DP Technology, Beijing 100080, People's Republic of China
| | - Weinan E
- AI for Science Institute, Beijing 100080, People's Republic of China
- Center for Machine Learning Research, School of Mathematical Sciences, Peking University, Beijing 100084, People's Republic of China
| | - Roberto Car
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, United States
- Department of Chemistry, Department of Physics, Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544, United States
| |
Collapse
|
36
|
Schütt KT, Hessmann SSP, Gebauer NWA, Lederer J, Gastegger M. SchNetPack 2.0: A neural network toolbox for atomistic machine learning. J Chem Phys 2023; 158:144801. [PMID: 37061495 DOI: 10.1063/5.0138367] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/17/2023] Open
Abstract
SchNetPack is a versatile neural network toolbox that addresses both the requirements of method development and the application of atomistic machine learning. Version 2.0 comes with an improved data pipeline, modules for equivariant neural networks, and a PyTorch implementation of molecular dynamics. An optional integration with PyTorch Lightning and the Hydra configuration framework powers a flexible command-line interface. This makes SchNetPack 2.0 easily extendable with a custom code and ready for complex training tasks, such as the generation of 3D molecular structures.
Collapse
Affiliation(s)
- Kristof T Schütt
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| | | | - Niklas W A Gebauer
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| | - Jonas Lederer
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| | - Michael Gastegger
- Machine Learning Group, Technische Universität Berlin, 10587 Berlin, Germany
| |
Collapse
|
37
|
Herzog B, Casier B, Lebègue S, Rocca D. Solving the Schrödinger Equation in the Configuration Space with Generative Machine Learning. J Chem Theory Comput 2023; 19:2484-2490. [PMID: 37043718 DOI: 10.1021/acs.jctc.2c01216] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/14/2023]
Abstract
The configuration interaction approach provides a conceptually simple and powerful approach to solve the Schrödinger equation for realistic molecules and materials but is characterized by an unfavorable scaling, which strongly limits its practical applicability. Effectively selecting only the configurations that actually contribute to the wave function is a fundamental step toward practical applications. We propose a machine learning approach that iteratively trains a generative model to preferentially generate the important configurations. By considering molecular applications it is shown that convergence to chemical accuracy can be achieved much more rapidly with respect to random sampling or the Monte Carlo configuration interaction method. This work paves the way to a broader use of generative models to solve the electronic structure problem.
Collapse
Affiliation(s)
- Basile Herzog
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Bastien Casier
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Sébastien Lebègue
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| | - Dario Rocca
- Université de Lorraine and CNRS, LPCT UMR 7019, F-54000 Nancy, France
| |
Collapse
|
38
|
Ren W, Fu W, Wu X, Chen J. Towards the ground state of molecules via diffusion Monte Carlo on neural networks. Nat Commun 2023; 14:1860. [PMID: 37012248 PMCID: PMC10070323 DOI: 10.1038/s41467-023-37609-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 03/20/2023] [Indexed: 04/05/2023] Open
Abstract
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. However, the inaccurate nodal structure hinders the application of DMC for more challenging electronic correlation problems. In this work, we apply the neural-network based trial wavefunction in fixed-node DMC, which allows accurate calculations of a broad range of atomic and molecular systems of different electronic characteristics. Our method is superior in both accuracy and efficiency compared to state-of-the-art neural network methods using variational Monte Carlo (VMC). We also introduce an extrapolation scheme based on the empirical linearity between VMC and DMC energies, and significantly improve our binding energy calculation. Overall, this computational framework provides a benchmark for accurate solutions of correlated electronic wavefunction and also sheds light on the chemical understanding of molecules.
Collapse
Affiliation(s)
- Weiluo Ren
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China.
| | - Weizhong Fu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
- School of Physics, Peking University, 100871, Beijing, People's Republic of China
| | - Xiaojie Wu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Ji Chen
- School of Physics, Peking University, 100871, Beijing, People's Republic of China.
- Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, 100871, Beijing, People's Republic of China.
| |
Collapse
|
39
|
Wheeler WA, Pathak S, Kleiner KG, Yuan S, Rodrigues JNB, Lorsung C, Krongchon K, Chang Y, Zhou Y, Busemeyer B, Williams KT, Muñoz A, Chow CY, Wagner LK. PyQMC: An all-Python real-space quantum Monte Carlo module in PySCF. J Chem Phys 2023; 158:114801. [PMID: 36948839 DOI: 10.1063/5.0139024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023] Open
Abstract
We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.
Collapse
Affiliation(s)
- William A Wheeler
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Shivesh Pathak
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - Kevin G Kleiner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Shunyue Yuan
- Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125, USA
| | - João N B Rodrigues
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC-UFABC, Santo André, São Paulo 09210-580, Brazil
| | - Cooper Lorsung
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Kittithat Krongchon
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Yueqing Chang
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Yiqing Zhou
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | | | | | - Alexander Muñoz
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Chun Yu Chow
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| |
Collapse
|
40
|
Cytter Y, Nandy A, Duan C, Kulik HJ. Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models. Phys Chem Chem Phys 2023; 25:8103-8116. [PMID: 36876903 DOI: 10.1039/d3cp00258f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023]
Abstract
Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.
Collapse
Affiliation(s)
- Yael Cytter
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Chenru Duan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA.,Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
| |
Collapse
|
41
|
Duan C, Nandy A, Terrones GG, Kastner DW, Kulik HJ. Active Learning Exploration of Transition-Metal Complexes to Discover Method-Insensitive and Synthetically Accessible Chromophores. JACS AU 2023; 3:391-401. [PMID: 36873700 PMCID: PMC9976347 DOI: 10.1021/jacsau.2c00547] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Revised: 11/15/2022] [Accepted: 11/16/2022] [Indexed: 06/18/2023]
Abstract
Transition-metal chromophores with earth-abundant transition metals are an important design target for their applications in lighting and nontoxic bioimaging, but their design is challenged by the scarcity of complexes that simultaneously have well-defined ground states and optimal target absorption energies in the visible region. Machine learning (ML) accelerated discovery could overcome such challenges by enabling the screening of a larger space but is limited by the fidelity of the data used in ML model training, which is typically from a single approximate density functional. To address this limitation, we search for consensus in predictions among 23 density functional approximations across multiple rungs of "Jacob's ladder". To accelerate the discovery of complexes with absorption energies in the visible region while minimizing the effect of low-lying excited states, we use two-dimensional (2D)efficient global optimization to sample candidate low-spin chromophores from multimillion complex spaces. Despite the scarcity (i.e., ∼0.01%) of potential chromophores in this large chemical space, we identify candidates with high likelihood (i.e., >10%) of computational validation as the ML models improve during active learning, representing a 1000-fold acceleration in discovery. Absorption spectra of promising chromophores from time-dependent density functional theory verify that 2/3 of candidates have the desired excited-state properties. The observation that constituent ligands from our leads have demonstrated interesting optical properties in the literature exemplifies the effectiveness of our construction of a realistic design space and active learning approach.
Collapse
Affiliation(s)
- Chenru Duan
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Chemistry, Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139, United States
| | - Aditya Nandy
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Chemistry, Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139, United States
| | - Gianmarco G. Terrones
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
| | - David W. Kastner
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Biological Engineering, Massachusetts
Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Heather J. Kulik
- Department
of Chemical Engineering, Massachusetts Institute
of Technology, Cambridge, Massachusetts 02139, United States
- Department
of Chemistry, Massachusetts Institute of
Technology, Cambridge, Massachusetts 02139, United States
| |
Collapse
|
42
|
Ghosh SK, Ghosh D. Machine learning matrix product state ansatz for strongly correlated systems. J Chem Phys 2023; 158:064108. [PMID: 36792489 DOI: 10.1063/5.0133399] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Abstract
Machine learning (ML) has been used to optimize the matrix product state (MPS) ansatz for the wavefunction of strongly correlated systems. The ML optimization of MPS has been tested for the Heisenberg Hamiltonian on one-dimensional and ladder lattices, which correspond to conjugated molecular systems. The input descriptors and output for the supervised ML are lattice configurations and configuration interaction coefficients, respectively. Efficient learning can be achieved from data over the full Hilbert space via exact diagonalization or full configuration interaction, as well as over a much smaller sub-space via Monte Carlo Configuration Interaction. We show that this circumvents the need to calculate energy and operator expectation values and is therefore a computationally efficient alternative to variational optimization.
Collapse
Affiliation(s)
- Sumanta K Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C. Mullick Road, Jadavpur, Kolkata 700032, India
| | - Debashree Ghosh
- School of Chemical Sciences, Indian Association for the Cultivation of Science, 2A and 2B Raja S. C. Mullick Road, Jadavpur, Kolkata 700032, India
| |
Collapse
|
43
|
Otis L, Neuscamman E. A promising intersection of excited‐state‐specific methods from quantum chemistry and quantum Monte Carlo. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2023. [DOI: 10.1002/wcms.1659] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Affiliation(s)
- Leon Otis
- Department of Physics University of California Berkeley Berkeley California USA
| | - Eric Neuscamman
- Department of Chemistry University of California Berkeley Berkeley California USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley California USA
| |
Collapse
|
44
|
Onder I, Secer A, Ozisik M, Bayram M. Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity. Heliyon 2023; 9:e13519. [PMID: 36814630 PMCID: PMC9939611 DOI: 10.1016/j.heliyon.2023.e13519] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2022] [Revised: 12/10/2022] [Accepted: 02/02/2023] [Indexed: 02/10/2023] Open
Abstract
We have discussed the perturbed Gerdjikov-Ivanov (pGI) equation describing optical pulse propagation (PP) with perturbation effects, which has various applications in optical fibers, especially in photonic crystal fibers. According to our literature review, we have discovered new and original soliton types using the Sardar sub-equation and the modified Kudryashov methods, which have not been applied to this model before. We obtained dark, bright, periodic-singular and periodic-M-shaped soliton solutions, respectively. The analytical forms of the obtained solutions are represented by 3D, 2D and contour graphics. In addition, the physical effects of the solution parameters on the wave envelope have been described and clearly interpreted by presenting their 2D graphics.
Collapse
Affiliation(s)
- Ismail Onder
- Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
| | - Aydin Secer
- Department of Computer Engineering, Biruni University, Istanbul, Turkey
| | - Muslum Ozisik
- Department of Mathematical Engineering, Yildiz Technical University, Istanbul, Turkey
| | - Mustafa Bayram
- Department of Computer Engineering, Biruni University, Istanbul, Turkey,Corresponding author.
| |
Collapse
|
45
|
Thie A, Menger MF, Faraji S. HOAX: a hyperparameter optimisation algorithm explorer for neural networks. Mol Phys 2023. [DOI: 10.1080/00268976.2023.2172732] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023]
Affiliation(s)
- Albert Thie
- Zernike Institute for Advanced Materials, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
| | - Maximilian F.S.J. Menger
- Zernike Institute for Advanced Materials, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
| | - Shirin Faraji
- Zernike Institute for Advanced Materials, Faculty of Science and Engineering, University of Groningen, Groningen, The Netherlands
| |
Collapse
|
46
|
Rigo M, Hall B, Hjorth-Jensen M, Lovato A, Pederiva F. Solving the nuclear pairing model with neural network quantum states. Phys Rev E 2023; 107:025310. [PMID: 36932590 DOI: 10.1103/physreve.107.025310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2022] [Accepted: 02/10/2023] [Indexed: 06/18/2023]
Abstract
We present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the ground-state wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically exact full configuration-interaction values.
Collapse
Affiliation(s)
- Mauro Rigo
- Physics Department, University of Trento, via Sommarive 14, I-38123 Trento, Italy
| | - Benjamin Hall
- Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA
- Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Morten Hjorth-Jensen
- Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University, East Lansing, Michigan 48824, USA
- Department of Physics and Center for Computing in Science Education, University of Oslo, N-0316 Oslo, Norway
| | - Alessandro Lovato
- Physics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
- INFN-TIFPA Trento Institute for Fundamental Physics and Applications, Via Sommarive, 14, 38123 Trento, Italy
| | - Francesco Pederiva
- Physics Department, University of Trento, via Sommarive 14, I-38123 Trento, Italy
- INFN-TIFPA Trento Institute for Fundamental Physics and Applications, Via Sommarive, 14, 38123 Trento, Italy
| |
Collapse
|
47
|
Cassella G, Sutterud H, Azadi S, Drummond ND, Pfau D, Spencer JS, Foulkes WMC. Discovering Quantum Phase Transitions with Fermionic Neural Networks. PHYSICAL REVIEW LETTERS 2023; 130:036401. [PMID: 36763402 DOI: 10.1103/physrevlett.130.036401] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 11/18/2022] [Indexed: 06/18/2023]
Abstract
Deep neural networks have been very successful as highly accurate wave function Ansätze for variational Monte Carlo calculations of molecular ground states. We present an extension of one such Ansatz, FermiNet, to calculations of the ground states of periodic Hamiltonians, and study the homogeneous electron gas. FermiNet calculations of the ground-state energies of small electron gas systems are in excellent agreement with previous initiator full configuration interaction quantum Monte Carlo and diffusion Monte Carlo calculations. We investigate the spin-polarized homogeneous electron gas and demonstrate that the same neural network architecture is capable of accurately representing both the delocalized Fermi liquid state and the localized Wigner crystal state. The network converges on the translationally invariant ground state at high density and spontaneously breaks the symmetry to produce the crystalline ground state at low density, despite being given no a priori knowledge that a phase transition exists.
Collapse
Affiliation(s)
- Gino Cassella
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Halvard Sutterud
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Sam Azadi
- Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom
| | - N D Drummond
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - David Pfau
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
- DeepMind, London N1C 4DJ, United Kingdom
| | | | - W M C Foulkes
- Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom
| |
Collapse
|
48
|
Electronic excited states in deep variational Monte Carlo. Nat Commun 2023; 14:274. [PMID: 36650151 PMCID: PMC9845370 DOI: 10.1038/s41467-022-35534-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 12/08/2022] [Indexed: 01/19/2023] Open
Abstract
Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method's potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods.
Collapse
|
49
|
Duan C, Nandy A, Meyer R, Arunachalam N, Kulik HJ. A transferable recommender approach for selecting the best density functional approximations in chemical discovery. NATURE COMPUTATIONAL SCIENCE 2023; 3:38-47. [PMID: 38177951 DOI: 10.1038/s43588-022-00384-0] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2022] [Accepted: 11/23/2022] [Indexed: 01/06/2024]
Abstract
Approximate density functional theory has become indispensable owing to its balanced cost-accuracy trade-off, including in large-scale screening. To date, however, no density functional approximation (DFA) with universal accuracy has been identified, leading to uncertainty in the quality of data generated from density functional theory. With electron density fitting and Δ-learning, we build a DFA recommender that selects the DFA with the lowest expected error with respect to the gold standard (but cost-prohibitive) coupled cluster theory in a system-specific manner. We demonstrate this recommender approach on the evaluation of vertical spin splitting energies of transition metal complexes. Our recommender predicts top-performing DFAs and yields excellent accuracy (about 2 kcal mol-1) for chemical discovery, outperforming both individual Δ-learning models and the best conventional single-functional approach from a set of 48 DFAs. By demonstrating transferability to diverse synthesized compounds, our recommender potentially addresses the accuracy versus scope dilemma broadly encountered in computational chemistry.
Collapse
Affiliation(s)
- Chenru Duan
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Aditya Nandy
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Ralf Meyer
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Naveen Arunachalam
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA.
| |
Collapse
|
50
|
Organic reaction mechanism classification using machine learning. Nature 2023; 613:689-695. [PMID: 36697863 DOI: 10.1038/s41586-022-05639-4] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2022] [Accepted: 12/08/2022] [Indexed: 01/26/2023]
Abstract
A mechanistic understanding of catalytic organic reactions is crucial for the design of new catalysts, modes of reactivity and the development of greener and more sustainable chemical processes1-13. Kinetic analysis lies at the core of mechanistic elucidation by facilitating direct testing of mechanistic hypotheses from experimental data. Traditionally, kinetic analysis has relied on the use of initial rates14, logarithmic plots and, more recently, visual kinetic methods15-18, in combination with mathematical rate law derivations. However, the derivation of rate laws and their interpretation require numerous mathematical approximations and, as a result, they are prone to human error and are limited to reaction networks with only a few steps operating under steady state. Here we show that a deep neural network model can be trained to analyse ordinary kinetic data and automatically elucidate the corresponding mechanism class, without any additional user input. The model identifies a wide variety of classes of mechanism with outstanding accuracy, including mechanisms out of steady state such as those involving catalyst activation and deactivation steps, and performs excellently even when the kinetic data contain substantial error or only a few time points. Our results demonstrate that artificial-intelligence-guided mechanism classification is a powerful new tool that can streamline and automate mechanistic elucidation. We are making this model freely available to the community and we anticipate that this work will lead to further advances in the development of fully automated organic reaction discovery and development.
Collapse
|