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Matin S, Allen AEA, Smith J, Lubbers N, Jadrich RB, Messerly R, Nebgen B, Li YW, Tretiak S, Barros K. Machine Learning Potentials with the Iterative Boltzmann Inversion: Training to Experiment. J Chem Theory Comput 2024. [PMID: 38307009 DOI: 10.1021/acs.jctc.3c01051] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2024]
Abstract
Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.
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Affiliation(s)
- Sakib Matin
- Department of Physics, Boston University, Boston, Massachusetts 02215, United States
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Alice E A Allen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Justin Smith
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- NVIDIA Corp., Santa Clara, California 95051, United States
| | - Nicholas Lubbers
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Ryan B Jadrich
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Richard Messerly
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Benjamin Nebgen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Ying Wai Li
- Computer, Computational, and Statistical Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Integrated Nanotechnologies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
| | - Kipton Barros
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
- Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87546, United States
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Manzhos S, Lüder J, Ihara M. Machine learning of kinetic energy densities with target and feature smoothing: Better results with fewer training data. J Chem Phys 2023; 159:234115. [PMID: 38112506 DOI: 10.1063/5.0175689] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Accepted: 11/27/2023] [Indexed: 12/21/2023] Open
Abstract
Machine learning (ML) of kinetic energy functionals (KEFs), in particular kinetic energy density (KED) functionals, is a promising way to construct KEFs for orbital-free density functional theory (DFT). Neural networks and kernel methods including Gaussian process regression (GPR) have been used to learn Kohn-Sham (KS) KED from density-based descriptors derived from KS DFT calculations. The descriptors are typically expressed as functions of different powers and derivatives of the electron density. This can generate large and extremely unevenly distributed datasets, which complicates effective application of ML techniques. Very uneven data distributions require many training datapoints, can cause overfitting, and can ultimately lower the quality of an ML KED model. We show that one can produce more accurate ML models from fewer data by working with smoothed density-dependent variables and KED. Smoothing palliates the issue of very uneven data distributions and associated difficulties of sampling while retaining enough spatial structure necessary for working within the paradigm of KEDF. We use GPR as a function of smoothed terms of the fourth order gradient expansion and KS effective potential and obtain accurate and stable (with respect to different random choices of training points) kinetic energy models for Al, Mg, and Si simultaneously from as few as 2000 samples (about 0.3% of the total KS DFT data). In particular, accuracies on the order of 1% in a measure of the quality of energy-volume dependence B'=EV0-ΔV-2EV0+E(V0+ΔV)ΔV/V02 (where V0 is the equilibrium volume and ΔV is a deviation from it) are obtained simultaneously for all three materials.
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Affiliation(s)
- Sergei Manzhos
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
| | - Johann Lüder
- Department of Materials and Optoelectronic Science, National Sun Yat-sen University, No. 70, Lien-Hai Road, Kaohsiung 80424, Taiwan
- Center of Crystal Research, National Sun Yat-sen University, No. 70, Lien-Hai Road, Kaohsiung 80424, Taiwan
- Center for Theoretical and Computational Physics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan
| | - Manabu Ihara
- School of Materials and Chemical Technology, Tokyo Institute of Technology, Ookayama 2-12-1, Meguro-ku, Tokyo 152-8552, Japan
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Lu D, Jiang W, Chen Y, Zhang L, Jia W, Wang H, Chen M. DP Compress: A Model Compression Scheme for Generating Efficient Deep Potential Models. J Chem Theory Comput 2022; 18:5559-5567. [PMID: 35926122 DOI: 10.1021/acs.jctc.2c00102] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning-based PES model. This scheme, we call DP Compress, is an efficient postprocessing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, H2O, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online.
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Affiliation(s)
- Denghui Lu
- HEDPS, CAPT, College of Engineering, Peking University, Beijing 100871, P. R. China
| | - Wanrun Jiang
- Songshan Lake Materials Laboratory, Dongguan, Guangdong 523808, P. R. China.,Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P. R. China
| | - Yixiao Chen
- Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, United States
| | - Linfeng Zhang
- Beijing Institute of Big Data Research, Beijing 100871, P. R. China
| | - Weile Jia
- Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, P. R. China.,University of Chinese Academy of Sciences, Beijing 100049, P. R. China
| | - Han Wang
- HEDPS, CAPT, College of Engineering, Peking University, Beijing 100871, P. R. China.,Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Fenghao East Road 2, Beijing 100094, P. R. China
| | - Mohan Chen
- HEDPS, CAPT, College of Engineering, Peking University, Beijing 100871, P. R. China
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Liu X, Zhang L, Liu J. Machine learning phase space quantum dynamics approaches. J Chem Phys 2021; 154:184104. [PMID: 34241027 DOI: 10.1063/5.0046689] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
Derived from phase space expressions of the quantum Liouville theorem, equilibrium continuity dynamics is a category of trajectory-based phase space dynamics methods, which satisfies the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (even of nonlinear operators) in the classical and harmonic limits. The effective force and effective mass matrix are important elements in the equations of motion of equilibrium continuity dynamics, where only the zeroth term of an exact series expansion of the phase space propagator is involved. We introduce a machine learning approach for fitting these elements in quantum phase space, leading to a much more efficient integration of the equations of motion. Proof-of-concept applications to realistic molecules demonstrate that machine learning phase space dynamics approaches are possible as well as competent in producing reasonably accurate results with a modest computation effort.
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Affiliation(s)
- Xinzijian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Linfeng Zhang
- Beijing Institute of Big Data Research, Beijing 100871, China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
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Automated discovery of a robust interatomic potential for aluminum. Nat Commun 2021; 12:1257. [PMID: 33623036 PMCID: PMC7902823 DOI: 10.1038/s41467-021-21376-0] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/12/2020] [Accepted: 01/15/2021] [Indexed: 11/22/2022] Open
Abstract
Machine learning, trained on quantum mechanics (QM) calculations, is a powerful tool for modeling potential energy surfaces. A critical factor is the quality and diversity of the training dataset. Here we present a highly automated approach to dataset construction and demonstrate the method by building a potential for elemental aluminum (ANI-Al). In our active learning scheme, the ML potential under development is used to drive non-equilibrium molecular dynamics simulations with time-varying applied temperatures. Whenever a configuration is reached for which the ML uncertainty is large, new QM data is collected. The ML model is periodically retrained on all available QM data. The final ANI-Al potential makes very accurate predictions of radial distribution function in melt, liquid-solid coexistence curve, and crystal properties such as defect energies and barriers. We perform a 1.3M atom shock simulation and show that ANI-Al force predictions shine in their agreement with new reference DFT calculations. The accuracy of a machine-learned potential is limited by the quality and diversity of the training dataset. Here the authors propose an active learning approach to automatically construct general purpose machine-learning potentials here demonstrated for the aluminum case.
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Liang W, Lu G, Yu J. Machine-Learning-Driven Simulations on Microstructure and Thermophysical Properties of MgCl 2-KCl Eutectic. ACS APPLIED MATERIALS & INTERFACES 2021; 13:4034-4042. [PMID: 33430593 DOI: 10.1021/acsami.0c20665] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Theoretical studies on the MgCl2-KCl eutectic heavily rely on ab initio calculations based on density functional theory (DFT). However, neither large-scale nor long-time calculations are feasible in the framework of the ab initio method, which makes it challenging to accurately predict some properties. To address this issue, a scheme based on ab initio calculation, deep neural networks, and machine learning is introduced. By training on high-quality data sets generated by ab initio calculations, a deep potential (DP) is constructed to describe the interaction between atoms. This work shows that the DP enables higher efficiency and similar accuracy relative to DFT. By performing molecular dynamics simulations with DP, the microstructure and thermophysical properties of the MgCl2-KCl eutectic (32:68 mol %) are investigated. The structural evolution with temperature is analyzed through partial radial distribution functions, coordination numbers, angular distribution functions, and structural factors. Meanwhile, the estimated thermophysical properties are discussed, including density, thermal expansion coefficient, shear viscosity, self-diffusion coefficient, and specific heat capacity. It reveals that the Mg2+ ions in this system have a distorted tetrahedral geometry rather than an octahedral one (with vacancies). The microstructure of the MgCl2-KCl eutectic shows the feature of medium-range order, and this feature will be enhanced at a higher temperature. All predicted thermophysical properties are in good agreement with the experimental results. The hydrodynamic radius determined from the shear viscosity and self-diffusion coefficient shows that the Mg2+ ions have a strong local structure and diffuse as if with an intact coordination shell. Overall, this work provides a thorough understanding of the microstructure and enriches the data of the thermophysical properties of the MgCl2-KCl eutectic.
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Affiliation(s)
- Wenshuo Liang
- School of Resources and Environmental Engineering, East China University of Science and Technology, Shanghai 200237, China
- National Engineering Research Center for Integrated Utilization of Salt Lake Resource, East China University of Science and Technology, Shanghai 200237, China
| | - Guimin Lu
- School of Resources and Environmental Engineering, East China University of Science and Technology, Shanghai 200237, China
- National Engineering Research Center for Integrated Utilization of Salt Lake Resource, East China University of Science and Technology, Shanghai 200237, China
| | - Jianguo Yu
- School of Resources and Environmental Engineering, East China University of Science and Technology, Shanghai 200237, China
- National Engineering Research Center for Integrated Utilization of Salt Lake Resource, East China University of Science and Technology, Shanghai 200237, China
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Dral PO, Owens A, Dral A, Csányi G. Hierarchical machine learning of potential energy surfaces. J Chem Phys 2020; 152:204110. [DOI: 10.1063/5.0006498] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Affiliation(s)
- Pavlo O. Dral
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Alec Owens
- Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom
| | - Alexey Dral
- BigData Team, 1A Tormoznoye Shosse Off 17, Yaroslavl, Yaroslavl 150022, Russian Federation
| | - Gábor Csányi
- Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
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Abstract
As the quantum chemistry (QC) community embraces machine learning (ML), the number of new methods and applications based on the combination of QC and ML is surging. In this Perspective, a view of the current state of affairs in this new and exciting research field is offered, challenges of using machine learning in quantum chemistry applications are described, and potential future developments are outlined. Specifically, examples of how machine learning is used to improve the accuracy and accelerate quantum chemical research are shown. Generalization and classification of existing techniques are provided to ease the navigation in the sea of literature and to guide researchers entering the field. The emphasis of this Perspective is on supervised machine learning.
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Affiliation(s)
- Pavlo O Dral
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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