1
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Wu Z, Zhou T. Structural Coarse-Graining via Multiobjective Optimization with Differentiable Simulation. J Chem Theory Comput 2024; 20:2605-2617. [PMID: 38483262 DOI: 10.1021/acs.jctc.3c01348] [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
In the realm of multiscale molecular simulations, structure-based coarse-graining is a prominent approach for creating efficient coarse-grained (CG) representations of soft matter systems, such as polymers. This involves optimizing CG interactions by matching static correlation functions of the corresponding degrees of freedom in all-atom (AA) models. Here, we present a versatile method, namely, differentiable coarse-graining (DiffCG), which combines multiobjective optimization and differentiable simulation. The DiffCG approach is capable of constructing robust CG models by iteratively optimizing the effective potentials to simultaneously match multiple target properties. We demonstrate our approach by concurrently optimizing bonded and nonbonded potentials of a CG model of polystyrene (PS) melts. The resulting CG-PS model effectively reproduces both the structural characteristics, such as the equilibrium probability distribution of microscopic degrees of freedom and the thermodynamic pressure of the AA counterpart. More importantly, leveraging the multiobjective optimization capability, we develop a precise and efficient CG model for PS melts that is transferable across a wide range of temperatures, i.e., from 400 to 600 K. It is achieved via optimizing a pairwise potential with nonlinear temperature dependence in the CG model to simultaneously match target data from AA-MD simulations at multiple thermodynamic states. The temperature transferable CG-PS model demonstrates its ability to accurately predict the radial distribution functions and density at different temperatures, including those that are not included in the target thermodynamic states. Our work opens up a promising route for developing accurate and transferable CG models of complex soft-matter systems through multiobjective optimization with differentiable simulation.
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Affiliation(s)
- Zhenghao Wu
- Department of Chemistry, Xi'an Jiaotong-Liverpool University, Suzhou, Jiangsu 215123, P. R. China
| | - Tianhang Zhou
- College of Carbon Neutrality Future Technology, State Key Laboratory of Heavy Oil Processing, China University of Petroleum (Beijing), Beijing 102249, P. R. China
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2
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Horn KP, Vazquez-Salazar LI, Koch CP, Meuwly M. Improving potential energy surfaces using measured Feshbach resonance states. SCIENCE ADVANCES 2024; 10:eadi6462. [PMID: 38427733 PMCID: PMC10906917 DOI: 10.1126/sciadv.adi6462] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2023] [Accepted: 01/29/2024] [Indexed: 03/03/2024]
Abstract
The structure and dynamics of a molecular system is governed by its potential energy surface (PES), representing the total energy as a function of the nuclear coordinates. Obtaining accurate potential energy surfaces is limited by the exponential scaling of Hilbert space, restricting quantitative predictions of experimental observables from first principles to small molecules with just a few electrons. Here, we present an explicitly physics-informed approach for improving and assessing the quality of families of PESs by modifying them through linear coordinate transformations based on experimental data. We demonstrate this "morphing" of the PES for the He - H2+ complex using recent comprehensive Feshbach resonance (FR) measurements for reference PESs at three different levels of quantum chemistry. In all cases, the positions and intensities of peaks in the energy distributions are improved. We find these observables to be mainly sensitive to the long-range part of the PES.
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Affiliation(s)
- Karl P. Horn
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
| | | | - Christiane P. Koch
- Dahlem Center for Complex Quantum Systems and Fachbereich Physik, Freie Universität Berlin, Arnimallee 14, D-14195 Berlin, Germany
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
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3
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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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4
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Wang K, Xu L, Shao W, Jin H, Wang Q, Ma M. A Multiple-Fidelity Method for Accurate Simulation of MoS 2 Properties Using JAX-ReaxFF and Neural Network Potentials. J Phys Chem Lett 2024; 15:371-379. [PMID: 38175525 DOI: 10.1021/acs.jpclett.3c03080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2024]
Abstract
Reactive force field (ReaxFF) is a commonly used force field for modeling chemical reactions at the atomic level. Recently, JAX-ReaxFF, combined with automatic differentiation, has been used to efficiently parametrize ReaxFF. However, its analytical formula may lead to inaccurate predictions. While neural network-based potentials (NNPs) trained on density functional theory-labeled data offer a more accurate method, it requires a large amount of training data to be trained from scratch. To overcome these issues, we present a multiple-fidelity method that combines JAX-ReaxFF and NNP and apply the method on MoS2, a promising two-dimensional semiconductor for flexible electronics. By incorporating implicit prior physical information, ReaxFF can serve as a cost-effective way to generate pretraining data, facilitating more accurate simulations of MoS2. Moreover, in the Mo-S-H system, the pretraining strategy can reduce root-mean-square errors of energy by 20%. This approach can be extended to a wide variety of material systems, accelerating their computational research.
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Affiliation(s)
- Kehan Wang
- State Key Laboratory of Tribology in Advanced Equipment (SKLT), Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
| | - Longkun Xu
- Samsung Research China - Beijing (SRC-B), Beijing 100102, China
| | - Wei Shao
- Samsung Research China - Beijing (SRC-B), Beijing 100102, China
| | - Haishun Jin
- Samsung Research China - Beijing (SRC-B), Beijing 100102, China
| | - Qiang Wang
- Samsung Research China - Beijing (SRC-B), Beijing 100102, China
| | - Ming Ma
- State Key Laboratory of Tribology in Advanced Equipment (SKLT), Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China
- Center for Nano and Micro Mechanics, Tsinghua University, Beijing 100084, China
- Institute of Superlubricity Technology, Research Institute of Tsinghua University in Shenzhen, Shenzhen 518063, Guangdong, China
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5
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Coste A, Slejko E, Zavadlav J, Praprotnik M. Developing an Implicit Solvation Machine Learning Model for Molecular Simulations of Ionic Media. J Chem Theory Comput 2024; 20:411-420. [PMID: 38118122 PMCID: PMC10782447 DOI: 10.1021/acs.jctc.3c00984] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Revised: 12/04/2023] [Accepted: 12/04/2023] [Indexed: 12/22/2023]
Abstract
Molecular dynamics (MD) simulations of biophysical systems require accurate modeling of their native environment, i.e., aqueous ionic solution, as it critically impacts the structure and function of biomolecules. On the other hand, the models should be computationally efficient to enable simulations of large spatiotemporal scales. Here, we present the deep implicit solvation model for sodium chloride solutions that satisfies both requirements. Owing to the use of the neural network potential, the model can capture the many-body potential of mean force, while the implicit water treatment renders the model inexpensive. We demonstrate our approach first for pure ionic solutions with concentrations ranging from physiological to 2 M. We then extend the model to capture the effective ion interactions in the vicinity and far away from a DNA molecule. In both cases, the structural properties are in good agreement with all-atom MD, showcasing a general methodology for the efficient and accurate modeling of ionic media.
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Affiliation(s)
- Amaury Coste
- Laboratory
for Molecular Modeling, National Institute of Chemistry, Ljubljana SI-1001, Slovenia
| | - Ema Slejko
- Laboratory
for Molecular Modeling, National Institute of Chemistry, Ljubljana SI-1001, Slovenia
- Department
of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia
| | - Julija Zavadlav
- Professorship
of Multiscale Modeling of Fluid Materials, TUM School of Engineering
and Design, Technical University of Munich, Garching Near Munich DE-85748, Germany
| | - Matej Praprotnik
- Laboratory
for Molecular Modeling, National Institute of Chemistry, Ljubljana SI-1001, Slovenia
- Department
of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana SI-1000, Slovenia
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6
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Perrone M, Capelli R, Empereur-mot C, Hassanali A, Pavan GM. Lessons Learned from Multiobjective Automatic Optimizations of Classical Three-Site Rigid Water Models Using Microscopic and Macroscopic Target Experimental Observables. JOURNAL OF CHEMICAL AND ENGINEERING DATA 2023; 68:3228-3241. [PMID: 38115916 PMCID: PMC10726314 DOI: 10.1021/acs.jced.3c00538] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 09/08/2023] [Revised: 11/17/2023] [Accepted: 11/21/2023] [Indexed: 12/21/2023]
Abstract
The development of accurate water models is of primary importance for molecular simulations. Despite their intrinsic approximations, three-site rigid water models are still ubiquitously used to simulate a variety of molecular systems. Automatic optimization approaches have been recently used to iteratively refine three-site water models to fit macroscopic (average) thermodynamic properties, providing state-of-the-art three-site models that still present some deviations from the liquid water properties. Here, we show the results obtained by automatically optimizing three-site rigid water models to fit a combination of microscopic and macroscopic experimental observables. We use Swarm-CG, a multiobjective particle-swarm-optimization algorithm, for training the models to reproduce the experimental radial distribution functions of liquid water at various temperatures (rich in microscopic-level information on, e.g., the local orientation and interactions of the water molecules). We systematically analyze the agreement of these models with experimental observables and the effect of adding macroscopic information to the training set. Our results demonstrate how adding microscopic-rich information in the training of water models allows one to achieve state-of-the-art accuracy in an efficient way. Limitations in the approach and in the approximated description of water in these three-site models are also discussed, providing a demonstrative case useful for the optimization of approximated molecular models, in general.
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Affiliation(s)
- Mattia Perrone
- Department
of Applied Science and Technology, Politecnico
di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, Italy
| | - Riccardo Capelli
- Department
of Biosciences, Università degli
Studi di Milano, Via Celoria 26, Milano I-20133, Italy
| | - Charly Empereur-mot
- Department
of Innovative Technologies, University of Applied Sciences and Arts
of Southern Switzerland, Polo Universitario
Lugano, Campus Est, Via
la Santa 1, Lugano-Viganello CH-6962, Switzerland
| | - Ali Hassanali
- The
Abdus Salam International Center for Theoretical Physics, Strada Costiera 11, Trieste 34151, Italy
| | - Giovanni M. Pavan
- Department
of Applied Science and Technology, Politecnico
di Torino, Corso Duca degli Abruzzi 24, Torino I-10129, Italy
- Department
of Innovative Technologies, University of Applied Sciences and Arts
of Southern Switzerland, Polo Universitario
Lugano, Campus Est, Via
la Santa 1, Lugano-Viganello CH-6962, Switzerland
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7
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Navarro C, Majewski M, De Fabritiis G. Top-Down Machine Learning of Coarse-Grained Protein Force Fields. J Chem Theory Comput 2023; 19:7518-7526. [PMID: 37874270 PMCID: PMC10777392 DOI: 10.1021/acs.jctc.3c00638] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Indexed: 10/25/2023]
Abstract
Developing accurate and efficient coarse-grained representations of proteins is crucial for understanding their folding, function, and interactions over extended time scales. Our methodology involves simulating proteins with molecular dynamics and utilizing the resulting trajectories to train a neural network potential through differentiable trajectory reweighting. Remarkably, this method requires only the native conformation of proteins, eliminating the need for labeled data derived from extensive simulations or memory-intensive end-to-end differentiable simulations. Once trained, the model can be employed to run parallel molecular dynamics simulations and sample folding events for proteins both within and beyond the training distribution, showcasing its extrapolation capabilities. By applying Markov state models, native-like conformations of the simulated proteins can be predicted from the coarse-grained simulations. Owing to its theoretical transferability and ability to use solely experimental static structures as training data, we anticipate that this approach will prove advantageous for developing new protein force fields and further advancing the study of protein dynamics, folding, and interactions.
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Affiliation(s)
- Carles Navarro
- Acellera
Labs, Doctor Trueta 183, 08005 Barcelona, Spain
| | | | - Gianni De Fabritiis
- Computational
Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003 Barcelona, Spain
- Acellera
Ltd., Devonshire House
582, Middlesex HA7 1JS, United Kingdom
- Institució
Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluis Companys 23, 08010 Barcelona, Spain
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8
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Nadkarni I, Wu H, Aluru NR. Data-Driven Approach to Coarse-Graining Simple Liquids in Confinement. J Chem Theory Comput 2023; 19:7358-7370. [PMID: 37791529 DOI: 10.1021/acs.jctc.3c00633] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/05/2023]
Abstract
We propose a data-driven framework for identifying coarse-grained (CG) Lennard-Jones (LJ) potential parameters in confined systems for simple liquids. Our approach involves the use of a Deep Neural Network (DNN) that is trained to approximate the solution of the Inverse Liquid State (ILST) problem for confined systems. The DNN model inherently incorporates essential physical characteristics specific to confined fluids, enabling an accurate prediction of inhomogeneity effects. By utilizing transfer learning, we predict single-site LJ potentials of simple multiatomic liquids confined in a slit-like channel, which effectively replicate both the fluid structure and molecular force of the target All-Atom (AA) system when the electrostatic interactions are not dominant. In addition, we showcase the synergy between the data-driven approach and the well-known Bottom-Up coarse-graining method utilizing Relative-Entropy (RE) Minimization. Through the sequential utilization of these two methods, the robustness of the iterative RE method is significantly augmented, leading to a remarkable enhancement in convergence.
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Affiliation(s)
- Ishan Nadkarni
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Haiyi Wu
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Narayana R Aluru
- Walker Department of Mechanical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States
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9
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Majewski M, Pérez A, Thölke P, Doerr S, Charron NE, Giorgino T, Husic BE, Clementi C, Noé F, De Fabritiis G. Machine learning coarse-grained potentials of protein thermodynamics. Nat Commun 2023; 14:5739. [PMID: 37714883 PMCID: PMC10504246 DOI: 10.1038/s41467-023-41343-1] [Citation(s) in RCA: 16] [Impact Index Per Article: 16.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/02/2023] [Accepted: 08/29/2023] [Indexed: 09/17/2023] Open
Abstract
A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach this problem by constructing coarse-grained molecular potentials based on artificial neural networks and grounded in statistical mechanics. For training, we build a unique dataset of unbiased all-atom molecular dynamics simulations of approximately 9 ms for twelve different proteins with multiple secondary structure arrangements. The coarse-grained models are capable of accelerating the dynamics by more than three orders of magnitude while preserving the thermodynamics of the systems. Coarse-grained simulations identify relevant structural states in the ensemble with comparable energetics to the all-atom systems. Furthermore, we show that a single coarse-grained potential can integrate all twelve proteins and can capture experimental structural features of mutated proteins. These results indicate that machine learning coarse-grained potentials could provide a feasible approach to simulate and understand protein dynamics.
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Affiliation(s)
- Maciej Majewski
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain
| | - Adrià Pérez
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain
| | - Philipp Thölke
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain
| | - Stefan Doerr
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain
| | - Nicholas E Charron
- Department of Physics, Rice University, Houston, TX, 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, TX, 77005, USA
- Department of Physics, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - Toni Giorgino
- Biophysics Institute, National Research Council (CNR-IBF), 20133, Milan, Italy
| | - Brooke E Husic
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
- Lewis Sigler Institute for Integrative Genomics, Princeton University, Princeton, NJ, 08540, USA
- Princeton Center for Theoretical Science, Princeton University, Princeton, NJ, 08540, USA
- Center for the Physics of Biological Function, Princeton University, Princeton, NJ, 08540, USA
| | - Cecilia Clementi
- Department of Physics, Rice University, Houston, TX, 77005, USA.
- Center for Theoretical Biological Physics, Rice University, Houston, TX, 77005, USA.
- Department of Physics, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Department of Chemistry, Rice University, Houston, TX, 77005, USA.
| | - Frank Noé
- Department of Physics, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Department of Chemistry, Rice University, Houston, TX, 77005, USA.
- Microsoft Research AI4Science, Karl-Liebknecht Str. 32, 10178, Berlin, Germany.
| | - Gianni De Fabritiis
- Computational Science Laboratory, Universitat Pompeu Fabra, Barcelona Biomedical Research Park (PRBB), Carrer Dr. Aiguader 88, 08003, Barcelona, Spain.
- Acellera Labs, Doctor Trueta 183, 08005, Barcelona, Spain.
- Institució Catalana de Recerca i Estudis Avançats (ICREA), Passeig Lluis Companys 23, 08010, Barcelona, Spain.
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10
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Wang X, Li J, Yang L, Chen F, Wang Y, Chang J, Chen J, Feng W, Zhang L, Yu K. DMFF: An Open-Source Automatic Differentiable Platform for Molecular Force Field Development and Molecular Dynamics Simulation. J Chem Theory Comput 2023; 19:5897-5909. [PMID: 37589304 DOI: 10.1021/acs.jctc.2c01297] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/18/2023]
Abstract
In the simulation of molecular systems, the underlying force field (FF) model plays an extremely important role in determining the reliability of the simulation. However, the quality of the state-of-the-art molecular force fields is still unsatisfactory in many cases, and the FF parameterization process largely relies on human experience, which is not scalable. To address this issue, we introduce DMFF, an open-source molecular FF development platform based on an automatic differentiation technique. DMFF serves as a powerful tool for both top-down and bottom-up FF development. Using DMFF, both energies/forces and thermodynamic quantities such as ensemble averages and free energies can be evaluated in a differentiable way, realizing an automatic, yet highly flexible FF optimization workflow. DMFF also eases the evaluation of forces and virial tensors for complicated advanced FFs, helping the fast validation of new models in molecular dynamics simulation. DMFF has been released as an open-source package under the LGPL-3.0 license and is available at https://github.com/deepmodeling/DMFF.
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Affiliation(s)
| | - Jichen Li
- DP Technology, Beijing 100080, P. R. China
| | - Lan Yang
- Tsinghua-Berkley Shenzhen Institute, Shenzhen, Guangdong 518055, P. R. China
| | | | | | | | - Junmin Chen
- Tsinghua-Berkley Shenzhen Institute, Shenzhen, Guangdong 518055, P. R. China
| | - Wei Feng
- DP Technology, Beijing 100080, P. R. China
| | - Linfeng Zhang
- AI for Science Institute, Beijing 100080, P. R. China
| | - Kuang Yu
- Tsinghua-Berkley Shenzhen Institute, Shenzhen, Guangdong 518055, P. R. China
- Tsinghua Shenzhen International Graduate School, Shenzhen, Guangdong 518055, P. R. China
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11
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Wellawatte GP, Hocky GM, White AD. Neural potentials of proteins extrapolate beyond training data. J Chem Phys 2023; 159:085103. [PMID: 37642255 PMCID: PMC10474891 DOI: 10.1063/5.0147240] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/20/2023] [Accepted: 07/31/2023] [Indexed: 08/31/2023] Open
Abstract
We evaluate neural network (NN) coarse-grained (CG) force fields compared to traditional CG molecular mechanics force fields. We conclude that NN force fields are able to extrapolate and sample from unseen regions of the free energy surface when trained with limited data. Our results come from 88 NN force fields trained on different combinations of clustered free energy surfaces from four protein mapped trajectories. We used a statistical measure named total variation similarity to assess the agreement between reference free energy surfaces from mapped atomistic simulations and CG simulations from trained NN force fields. Our conclusions support the hypothesis that NN CG force fields trained with samples from one region of the proteins' free energy surface can, indeed, extrapolate to unseen regions. Additionally, the force matching error was found to only be weakly correlated with a force field's ability to reconstruct the correct free energy surface.
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Affiliation(s)
- Geemi P. Wellawatte
- Department of Chemistry, University of Rochester, Rochester, New York 14627, USA
| | - Glen M. Hocky
- Department of Chemistry, Simons Center for Computational Physical Chemistry, New York University, New York, New York 10003, USA
| | - Andrew D. White
- Department of Chemical Engineering, University of Rochester, Rochester, New York 14627, USA
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12
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Tkachenko NV, Tkachenko AA, Nebgen B, Tretiak S, Boldyrev AI. Neural network atomistic potentials for global energy minima search in carbon clusters. Phys Chem Chem Phys 2023; 25:21173-21182. [PMID: 37490276 DOI: 10.1039/d3cp02317f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/26/2023]
Abstract
The global energy optimization problem is an acute and important problem in chemistry. It is crucial to know the geometry of the lowest energy isomer (global minimum, GM) of a given compound for the evaluation of its chemical and physical properties. This problem is especially relevant for atomic clusters. Due to the exponential growth of the number of local minima geometries with the increase of the number of atoms in the cluster, it is important to find a computationally efficient and reliable method to navigate the energy landscape and locate a true global minima structure. Newly developed neural network (NN) atomistic potentials offer a numerically efficient and relatively accurate approach for molecular structure optimization. An important question that needs to be answered is "Can NN potentials, trained on a given set, represent the potential energy surface (PES) of a neighboring domain?". In this work, we tested the applicability of ANI-1ccx and ANI-nr NN atomistic potentials for the global minima optimization of carbon clusters Cn (n = 3-10). We showed that with the introduction of the cluster connectivity restriction and consequent DFT or ab initio calculations, ANI-1ccx and ANI-nr can be considered as robust PES pre-samplers that can capture the GM structure even for large clusters such as C20.
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Affiliation(s)
- Nikolay V Tkachenko
- Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300, USA.
| | | | - Benjamin Nebgen
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Sergei Tretiak
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
| | - Alexander I Boldyrev
- Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300, USA.
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13
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Zaporozhets I, Clementi C. Multibody Terms in Protein Coarse-Grained Models: A Top-Down Perspective. J Phys Chem B 2023; 127:6920-6927. [PMID: 37499123 DOI: 10.1021/acs.jpcb.3c04493] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/29/2023]
Abstract
Coarse-grained models allow computational investigation of biomolecular processes occurring on long time and length scales, intractable with atomistic simulation. Traditionally, many coarse-grained models rely mostly on pairwise interaction potentials. However, the decimation of degrees of freedom should, in principle, lead to a complex many-body effective interaction potential. In this work, we use experimental data on mutant stability to parametrize coarse-grained models for two proteins with and without many-body terms. We demonstrate that many-body terms are necessary to reproduce quantitatively the effects of point mutations on protein stability, particularly to implicitly take into account the effect of the solvent.
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Affiliation(s)
- Iryna Zaporozhets
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, 6100 Main Street, Houston, Texas 77005, United States
- Department of Physics, Freie Universität, Arnimallee 12, Berlin 14195, Germany
| | - Cecilia Clementi
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, 6100 Main Street, Houston, Texas 77005, United States
- Department of Physics, Freie Universität, Arnimallee 12, Berlin 14195, Germany
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14
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Bhatia H, Aydin F, Carpenter TS, Lightstone FC, Bremer PT, Ingólfsson HI, Nissley DV, Streitz FH. The confluence of machine learning and multiscale simulations. Curr Opin Struct Biol 2023; 80:102569. [PMID: 36966691 DOI: 10.1016/j.sbi.2023.102569] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/14/2022] [Revised: 01/31/2023] [Accepted: 02/08/2023] [Indexed: 06/04/2023]
Abstract
Multiscale modeling has a long history of use in structural biology, as computational biologists strive to overcome the time- and length-scale limits of atomistic molecular dynamics. Contemporary machine learning techniques, such as deep learning, have promoted advances in virtually every field of science and engineering and are revitalizing the traditional notions of multiscale modeling. Deep learning has found success in various approaches for distilling information from fine-scale models, such as building surrogate models and guiding the development of coarse-grained potentials. However, perhaps its most powerful use in multiscale modeling is in defining latent spaces that enable efficient exploration of conformational space. This confluence of machine learning and multiscale simulation with modern high-performance computing promises a new era of discovery and innovation in structural biology.
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Affiliation(s)
- Harsh Bhatia
- Computing Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA. https://twitter.com/@harshbhatia85
| | - Fikret Aydin
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Timothy S Carpenter
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Felice C Lightstone
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Peer-Timo Bremer
- Computing Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Helgi I Ingólfsson
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA
| | - Dwight V Nissley
- RAS Initiative, The Cancer Research Technology Program, Frederick National Laboratory, Frederick, MD, 21701, USA.
| | - Frederick H Streitz
- Physical and Life Sciences (PLS) Directorate, Lawrence Livermore National Laboratory, Livermore, CA, 94550, USA.
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15
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Krämer A, Durumeric AEP, Charron NE, Chen Y, Clementi C, Noé F. Statistically Optimal Force Aggregation for Coarse-Graining Molecular Dynamics. J Phys Chem Lett 2023; 14:3970-3979. [PMID: 37079800 DOI: 10.1021/acs.jpclett.3c00444] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/03/2023]
Abstract
Machine-learned coarse-grained (CG) models have the potential for simulating large molecular complexes beyond what is possible with atomistic molecular dynamics. However, training accurate CG models remains a challenge. A widely used methodology for learning bottom-up CG force fields maps forces from all-atom molecular dynamics to the CG representation and matches them with a CG force field on average. We show that there is flexibility in how to map all-atom forces to the CG representation and that the most commonly used mapping methods are statistically inefficient and potentially even incorrect in the presence of constraints in the all-atom simulation. We define an optimization statement for force mappings and demonstrate that substantially improved CG force fields can be learned from the same simulation data when using optimized force maps. The method is demonstrated on the miniproteins chignolin and tryptophan cage and published as open-source code.
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Affiliation(s)
- Andreas Krämer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Aleksander E P Durumeric
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Nicholas E Charron
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251, United States
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Yaoyi Chen
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- International Max Planck Research School for Biology and Computation (IMPRS-BAC), Max Planck Institute for Molecular Genetics, 14195 Berlin, Germany
| | - Cecilia Clementi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77251, United States
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Microsoft Research AI4Science, Karl-Liebknecht Straße 32, 10178 Berlin, Germany
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16
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Durumeric AEP, Charron NE, Templeton C, Musil F, Bonneau K, Pasos-Trejo AS, Chen Y, Kelkar A, Noé F, Clementi C. Machine learned coarse-grained protein force-fields: Are we there yet? Curr Opin Struct Biol 2023; 79:102533. [PMID: 36731338 PMCID: PMC10023382 DOI: 10.1016/j.sbi.2023.102533] [Citation(s) in RCA: 17] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2022] [Revised: 12/14/2022] [Accepted: 12/18/2022] [Indexed: 02/04/2023]
Abstract
The successful recent application of machine learning methods to scientific problems includes the learning of flexible and accurate atomic-level force-fields for materials and biomolecules from quantum chemical data. In parallel, the machine learning of force-fields at coarser resolutions is rapidly gaining relevance as an efficient way to represent the higher-body interactions needed in coarse-grained force-fields to compensate for the omitted degrees of freedom. Coarse-grained models are important for the study of systems at time and length scales exceeding those of atomistic simulations. However, the development of transferable coarse-grained models via machine learning still presents significant challenges. Here, we discuss recent developments in this field and current efforts to address the remaining challenges.
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Affiliation(s)
- Aleksander E P Durumeric
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - Nicholas E Charron
- Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, 77005, Texas, USA; Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany; Center for Theoretical Biological Physics, Rice University, 6100 Main Street, Houston, 77005, Texas, USA
| | - Clark Templeton
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany. https://twitter.com/pbrun03
| | - Félix Musil
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany. https://twitter.com/FelixMusil
| | - Klara Bonneau
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - Aldo S Pasos-Trejo
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany. https://twitter.com/sayeg84
| | - Yaoyi Chen
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany. https://twitter.com/hello_yaoyi
| | - Atharva Kelkar
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - Frank Noé
- Microsoft Research AI4Science, Karl-Liebknecht Str. 32, Berlin, 10178, Berlin, Germany; Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany; Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany; Department of Chemistry, Rice University, 6100 Main Street, Houston, 77005, Texas, USA. https://twitter.com/FrankNoeBerlin
| | - Cecilia Clementi
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195, Berlin, Germany; Center for Theoretical Biological Physics, Rice University, 6100 Main Street, Houston, 77005, Texas, USA; Department of Chemistry, Rice University, 6100 Main Street, Houston, 77005, Texas, USA; Department of Physics and Astronomy, Rice University, 6100 Main Street, Houston, 77005, Texas, USA.
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17
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Wang W, Wu Z, Dietschreit JCB, Gómez-Bombarelli R. Learning pair potentials using differentiable simulations. J Chem Phys 2023; 158:044113. [PMID: 36725529 DOI: 10.1063/5.0126475] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
Learning pair interactions from experimental or simulation data is of great interest for molecular simulations. We propose a general stochastic method for learning pair interactions from data using differentiable simulations (DiffSim). DiffSim defines a loss function based on structural observables, such as the radial distribution function, through molecular dynamics (MD) simulations. The interaction potentials are then learned directly by stochastic gradient descent, using backpropagation to calculate the gradient of the structural loss metric with respect to the interaction potential through the MD simulation. This gradient-based method is flexible and can be configured to simulate and optimize multiple systems simultaneously. For example, it is possible to simultaneously learn potentials for different temperatures or for different compositions. We demonstrate the approach by recovering simple pair potentials, such as Lennard-Jones systems, from radial distribution functions. We find that DiffSim can be used to probe a wider functional space of pair potentials compared with traditional methods like iterative Boltzmann inversion. We show that our methods can be used to simultaneously fit potentials for simulations at different compositions and temperatures to improve the transferability of the learned potentials.
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Affiliation(s)
- Wujie Wang
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Zhenghao Wu
- Eduard-Zintl-Institut für Anorganische und Physikalische Chemie, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany
| | - Johannes C B Dietschreit
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Rafael Gómez-Bombarelli
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
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18
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Thaler S, Stupp M, Zavadlav J. Deep coarse-grained potentials via relative entropy minimization. J Chem Phys 2022; 157:244103. [PMID: 36586977 DOI: 10.1063/5.0124538] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022] Open
Abstract
Neural network (NN) potentials are a natural choice for coarse-grained (CG) models. Their many-body capacity allows highly accurate approximations of the potential of mean force, promising CG simulations of unprecedented accuracy. CG NN potentials trained bottom-up via force matching (FM), however, suffer from finite data effects: They rely on prior potentials for physically sound predictions outside the training data domain, and the corresponding free energy surface is sensitive to errors in the transition regions. The standard alternative to FM for classical potentials is relative entropy (RE) minimization, which has not yet been applied to NN potentials. In this work, we demonstrate, for benchmark problems of liquid water and alanine dipeptide, that RE training is more data efficient, due to accessing the CG distribution during training, resulting in improved free energy surfaces and reduced sensitivity to prior potentials. In addition, RE learns to correct time integration errors, allowing larger time steps in CG molecular dynamics simulation, while maintaining accuracy. Thus, our findings support the use of training objectives beyond FM, as a promising direction for improving CG NN potential's accuracy and reliability.
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Affiliation(s)
- Stephan Thaler
- Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich, Munich, Germany
| | - Maximilian Stupp
- Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich, Munich, Germany
| | - Julija Zavadlav
- Multiscale Modeling of Fluid Materials, Department of Engineering Physics and Computation, TUM School of Engineering and Design, Technical University of Munich, Munich, Germany
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19
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Antila HS, Kav B, Miettinen MS, Martinez-Seara H, Jungwirth P, Ollila OHS. Emerging Era of Biomolecular Membrane Simulations: Automated Physically-Justified Force Field Development and Quality-Evaluated Databanks. J Phys Chem B 2022. [DOI: 10.1021/acs.jpcb.2c01954] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- Hanne S. Antila
- Department of Biomaterials, Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany
| | - Batuhan Kav
- Institute of Biological Information Processing, Structural Biochemistry (IBI-7), Forschungszentrum
Jülich, Wilhelm-Johnen-Str., 52425 Jülich, Germany
| | - Markus S. Miettinen
- Computational Biology Unit, Department of Informatics, University of Bergen, 5008 Bergen, Norway
- Department of Chemistry, University of Bergen, 5020 Bergen, Norway
| | - Hector Martinez-Seara
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo nam. 2, 16000 Prague 6, Czech Republic
| | - Pavel Jungwirth
- Institute of Organic Chemistry and Biochemistry, Czech Academy of Sciences, Flemingovo nam. 2, 16000 Prague 6, Czech Republic
| | - O. H. Samuli Ollila
- Institute of Biotechonology, University of Helsinki, Helsinki 00014, Finland
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20
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Mayr F, Harth M, Kouroudis I, Rinderle M, Gagliardi A. Machine Learning and Optoelectronic Materials Discovery: A Growing Synergy. J Phys Chem Lett 2022; 13:1940-1951. [PMID: 35188778 DOI: 10.1021/acs.jpclett.1c04223] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Novel optoelectronic materials have the potential to revolutionize the ongoing green transition by both providing more efficient photovoltaic (PV) devices and lowering energy consumption of devices like LEDs and sensors. The lead candidate materials for these applications are both organic semiconductors and more recently perovskites. This Perspective illustrates how novel machine learning techniques can help explore these materials, from speeding up ab initio calculations toward experimental guidance. Furthermore, based on existing work, perspectives around machine-learned molecular dynamics potentials, physically informed neural networks, and generative methods are outlined.
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Affiliation(s)
- Felix Mayr
- Department of Electrical and Computer Engineering, Technical University of Munich, Hans-Piloty-Straße 1, 85748 Garching bei München, Germany
| | - Milan Harth
- Department of Electrical and Computer Engineering, Technical University of Munich, Hans-Piloty-Straße 1, 85748 Garching bei München, Germany
| | - Ioannis Kouroudis
- Department of Electrical and Computer Engineering, Technical University of Munich, Hans-Piloty-Straße 1, 85748 Garching bei München, Germany
| | - Michael Rinderle
- Department of Electrical and Computer Engineering, Technical University of Munich, Hans-Piloty-Straße 1, 85748 Garching bei München, Germany
| | - Alessio Gagliardi
- Department of Electrical and Computer Engineering, Technical University of Munich, Hans-Piloty-Straße 1, 85748 Garching bei München, Germany
- Munich Data Science Institute, Technical University of Munich, Walther-von-Dyck-Straße 10, 85748 Garching bei München, Germany
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21
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Xu P, Mou X, Guo Q, Fu T, Ren H, Wang G, Li Y, Li G. Coarse-grained molecular dynamics study based on TorchMD. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2110218] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Peijun Xu
- Liaoning Normal University, Dalian 116029, China
| | - Xiaohong Mou
- Liaoning Normal University, Dalian 116029, China
| | - Qiuhan Guo
- Liaoning Normal University, Dalian 116029, China
| | - Ting Fu
- Pharmacy Department of Affiliated Zhongshan Hospital of Dalian University, Dalian 116001, China
| | - Hong Ren
- Department of Ophthalmology Aerospace Center Hospital, Beijing 100049, China
| | - Guiyan Wang
- Dalian Ocean University, Dalian 116029, China
| | - Yan Li
- Dalian Institute of Chemical Physics, State Key Laboratory of Molecular Reaction Dynamics, Dalian 116023, China
| | - Guohui Li
- Dalian Institute of Chemical Physics, State Key Laboratory of Molecular Reaction Dynamics, Dalian 116023, China
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