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Machine Learning for Atomistic Simulation

This document aims to serve as a concise overview of literature that discusses the application of machine learning to the problem of atomistic simulation. It is not a comprehensive index but rather aims to provide a sense of the development of the field and highlight key papers.

Please feel free to open an issue or pull requests.

Table of Contents

Embeddings and Representations

Below are various techniques for representing atomic systems and materials in a manner that is intended for usage with machine learning systems.

Atomic Cluster Expansion (ACE)

Title & Link Author(s) Pub. Date
Atomic cluster expansion for accurate and transferable interatomic potentials Drautz Jan 2019
Atomic cluster expansion of scalar, vectorial and tensorial properties and including magnetism and charge transfer Drautz Feb 2020
Performant implementation of the atomic cluster expansion: Application to copper and silicon Lysogorskiy, van der Oord, Bochkarev, Menon, Rinaldi, Hammerschmidt, Mrovec, Thompson, Csányi, Ortner, Drautz Mar 2021
Efficient parametrization of the atomic cluster expansion Bochkarev, Lysogorskiy, Menon, Qamar, Mrovec, Drautz Jan 2022
Atomic cluster expansion: Completeness, efficiency and stability Dusson, Bachmayr, Csanyi, Drautz, Etter, van der Oord, Ortner Apr 2022
Multilayer atomic cluster expansion for semi-local interactions Bochkarev, Lysogorskiy, Ortner, Csanyi, Drautz May 2022
Atomic cluster expansion and wave function representations Drautz, Ortner Jun 2022
Permutation-adapted complete and independent basis for atomic cluster expansion descriptors Goff, Sievers, Wood, Thompson Aug 2022

Smooth Overlap of Atomic Position (SOAP)

Title & Link Author(s) Pub. Date
On representing chemical environments Bartok, Kondor, Csanyi Mar 2013
Comparing molecules and solids across structural and alchemical space De, Bartok, Csanyi, Ceriotti Apr 2016
Automatic Selection of Atomic Fingerprints and Reference Configurations for Machine-Learning Potentials Imbalzano, Anelli, Giofré, Klees, Behler, Ceriotti Apr 2018
Machine-learning of atomic-scale properties based on physical principles Ceriotti, Willatt, Csányi Jan 2019
Atom-density representations for machine learning Willatt, Musil, Ceriotti Apr 2019
Atomic-scale representation and statistical learning of tensorial properties Grisafi, Wilkins, Willatt, Ceriotti Apr 2019
Optimizing many-body atomic descriptors for enhanced computational performance of machine learning based interatomic potentials Caro May 2019
Efficient implementation of atom-density representations Musil, Veit, Goscinski, Fraux, Willatt, Stricker, Junge, Ceriotti Jan 2021

Gaussian Approximation Potentials (GAP)

(Many applications paper omitted; please see here for a more comprehensive list)

Title & Link Author(s) Pub. Date
Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons Bartok, Payne, Kondor, Csanyi Oct 2009
Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics Bartok Mar 2010
Accuracy and transferability of GAP models for tungsten Szlachta, Bartok, Csanyi May 2014
Localized Coulomb Descriptors for the Gaussian Approximation Potential Barker, Bulin, Hamaekers, Mathias Nov 2016
Many-Body Coarse-Grained Interactions using Gaussian Approximation Potentials John Nov 2016
Machine-learned Interatomic Potentials for Alloys and Alloy Phase Diagrams Rosenbrock, Gubaev, Shapeev, Pártay, Bernstein, Csányi, Hart Jun 2019
Combining phonon accuracy with high transferability in Gaussian approximation potential models George, Hautier, Bartok, Csanyi, Deringer May 2020
Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials Zaverkin, Kastner July 2020
Massively Parallel Fitting of Gaussian Approximation Potentials Klawohn, Kermode, Bartók Jul 2022
Atomistic structure search using local surrogate mode Rønne, Christiansen, Slavensky, Tang, Brix, Pedersen, Bisbo, Hammer Aug 2022

Moment Tensor Potentials (MTP)

Title & Link Author(s) Pub. Date
Moment Tensor Potentials: a class of systematically improvable interatomic potentials Shapeev Dec 2015
Moment tensor Potentials as a Promising Tool to Study Diffusion Processes Novoselov, Yanilkin, Shapeev, Podryabinkin Dec 2018
Machine-learning potentials enable predictive and tractable high-throughput screening of random alloys Hodapp, Shapeev Jul 2021

Atom-Centered Symmetry Functions (ACSF)

Title & Link Author(s) Pub. Date
Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces Behler, Parrinello Apr 2007
Atom-centered symmetry functions for constructing high-dimensional neural network potentials Behler Feb 2011
An implementation of artificial neural-network potentials for atomistic materials simulations: Performance for TiO2 (aenet) Artrith, Urban Mar 2016
Amp: A modular approach to machine learning in atomistic simulations Khorshidi, Peterson Oct 2016
Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species Artrith, Urban, Ceder Jul 2017
wACSF—Weighted atom-centered symmetry functions as descriptors in machine learning potentials Gastegger, Schwiedrzik, Bittermann, Berzsenyi, Marquetand Mar 2018
Optimized symmetry functions for machine-learning interatomic potentials of multicomponent systems Rostami, Amsler, Ghasemi Sep 2018
Augmenting machine learning of energy landscapes with local structural information Honrao, Xie, Hennig Aug 2020
A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer Wai Ko, Finkler, Goedecker, Behler Jan 2021
Unified theory of atom-centered representations and message-passing machine-learning schemes Nigam, Pozdnyakov, Fraux May 2022

FCHL

(Acronym based off of initial authors' last names)

Title & Link Author(s) Pub. Date
Alchemical and structural distribution based representation for universal quantum machine learning Faber, Christensen, Huang, von Lilienfeld Mar 2018
FCHL revisited: Faster and more accurate quantum machine learning Christensen, Bratholm, Faber, von Lilienfeld Jan 2020

Wavelet Scattering

Title & Link Author(s) Pub. Date
Solid harmonic wavelet scattering Eickenberg, Exarchakis, Hirn, Mallat Dec 2017
Steerable Wavelet Scattering for 3D Atomic Systems with Application to Li-Si Energy Prediction Brumwell, Sinz, Jin Kim, Qi, Hirn Nov 2018
Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties Sinz, Swift, Brumwell, Liu, Jin Kim, Qi, Hirn Jun 2020

Miscellaneous

Title & Link Author(s) Pub. Date
Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks Pukrittayakamee, Malshe, Hagan, Raff, Narulkar, Bukkapatnum, Komanduri Apr 2009
Fourier series of atomic radial distribution functions: A molecular fingerprint for machine learning models of quantum chemical properties von Lilienfeld, Ramakrishnan, Rupp, Knoll Jul 2013
How to represent crystal structures for machine learning: Towards fast prediction of electronic properties Schutt, Glawe, Brockherde, Sanna, Muller, Gross May 2014
A fingerprint based metric for measuring similarities of crystalline structures Zhu, Amsler, Fuhrer, Schaefer, Faraji, Rostami, Ghasemi, Sadeghi, Grauzinyte, Wolverton, Goedecker Jan 2016
Unified Representation of Molecules and Crystals for Machine Learning (MBTR) Huo, Rupp Apr 2017
An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields Tang, Zhang, Karniadakis Dec 2017
A novel approach to describe chemical environments in high-dimensional neural network potentials Kocer, Mason, Erturk Mar 2019
Embedded Atom Neural Network Potentials: Efficient and Accurate Machine Learning with a Physically Inspired Representation (EAM) Zhang, Hu, Jiang Aug 2019
Continuous and optimally complete description of chemical environments using Spherical Bessel descriptors (SB) Kocer, Mason, Erturk Jan 2020
TUCAN: A molecular identifier and descriptor applicable to the whole periodic table from hydrogen to oganesson Brammer, Blanke, Kellner, Hoffmann, Herres-Pawlis, Schatzschneider Mar 2022

Meta-literature

Title & Link Author(s) Pub. Date
SISSO: A compressed-sensing method for identifying the best low-dimensional descriptor in an immensity of offered candidates Ouyang, Curtarolo, Ahmetcik, Scheffler, Ghiringhelli Aug 2018
A Performance and Cost Assessment of Machine Learning Interatomic Potentials Zuo, Chen, Li, Deng, Chen, Behler, Csányi, Shapeev, Thompson, Wood, Ong Jul 2019
DScribe: Library of descriptors for machine learning in materials science Himanen, Jäger, Morooka, Canova, Ranawat, Gao, Rinke, Foster Nov 2019
Descriptors representing two- and three-body atomic distributions and their effects on the accuracy of machine-learned interatomic potentials Jinnouchi, Karsai, Verdi, Asahi, Kresse Apr 2020
Sensitivity and Dimensionality of Atomic Environment Representations used for Machine Learning Interatomic Potentials Onat, Ortner, Kermode Jun 2020
An assessment of the structural resolution of various fingerprints commonly used in machine learning Karamad, Magar, Shi, Siahrostami, Gates, Farimani Aug 2020
Incompleteness of Atomic Structure Representations Pozdnyakov, Willatt, Bartok, Ortner, Csanyi, Ceriotti Oct 2020
Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions Parsaeifard, Goedecker Feb 2021
The role of feature space in atomistic learning Goscinski, Fraux, Imbalzano, Ceriotti Apr 2021
Strategies for the Construction of Machine-Learning Potentials for Accurate and Efficient Atomic-Scale Simulations Miksch, Morawietz, Kästner, Urban, Artrith May 2021
Compressing local atomic neighbourhood descriptors Darby, Kermode, Csányi Dec 2021

Tools and Architectures

These are methods and networks that are intended to process materials or molecular data for the purposes of atomistic simulation (occasionally, property prediction)

e3nn Precursor

These works were developed independently of each other but propose very similar ideas which were mostly consolidated into the e3nn framework.

Title & Link Author(s) Pub. Date
Group Equivariant Convolutional Networks Cohen, Welling Feb 2016
Spherical CNNs Cohen, Geiger, Koehler, Welling Jan 2018
Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds Smidt, Thomas, Kearnes, Yang, Li, Kohlhoff, Riley Feb 2018
N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials Kondor Mar 2018
Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network Kondor, Lin, Trivedi Jun 2018
3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data Weiler, Geiger, Welling, Boomsma, Cohen Jul 2018
SE(3)-Equivariant prediction of molecular wavefunctions and electronic densities Unke, Bogojeski, Gastegger, Geiger, Smidt, Müller Jun 2021

e3nn

Title & Link Author(s) Pub. Date
Finding symmetry breaking order parameters with Euclidean neural networks Smidt, Geiger, Miller Jul 2020
Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties Miller, Geiger, Smidt, Noe Aug 2020
E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials (NequIP) Batzner, Musaelian, Sun, Geiger, Mailoa, Kornbluth, Molinari, Smidt, Kozinsky Jan 2021]
Direct Prediction of Phonon Density of States With Euclidean Neural Networks Chen, Andrejevic, Smidt, Z. Ding, Q. Xu, Y. Chi, Q. Nguyen, Alatas, Kong, M. Li Mar 2021
Cracking the Quantum Scaling Limit with Machine Learned Electron Densities Rackers, Tecot, Geiger, Smidt Jan 2022
Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics (Allegro) Musaelian, Batzner, Johansson, Sun, Owen, Kornbluth, Kozinsky Apr 2022
The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials (BOTNet) Batatia, Batzner, Kovács, Musaelian, Simm, Drautz, Ortner, Kozinsky, Csányi May 2022
MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields Batatia, Kovács, Simm, Ortner, Csányi Jun 2022
Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs Liao, Smidt Jun 2022
e3nn: Euclidean Neural Networks Geiger, Smidt Jul 2022
Machine Learning Magnetism Classifiers from Atomic Coordinates Merker, Heiberger, Q. Nguyen, Liu, Chen, Andrejevic, Drucker, Okabe, S.E. Kim, Wang, Smidt, M. Li Sep 2022
High Accuracy Uncertainty-Aware Interatomic Force Modeling with Equivariant Bayesian Neural Networks Rensmeyer, Craig, Kramer, Niggemann Apr 2023

Equivariant Graph Neural Networks (EGNN)

Title & Link Author(s) Pub. Date
E(n)-Equivariant Graph Neural Networks Satorras, Hoogeboom, Welling Feb 2021
E(n)-Equivariant Normalizing Flows Satorras, Hoogeboom, Fuchs, Posner, Welling May 2021
Geometric and Physical Quantities Improve E(3)-Equivariant Message Passing (SEGNN) Brandstetter, Hesselink, Pol, Bekkers, Welling Oct 2021

SchNet

Title & Link Author(s) Pub. Date
SchNet: A continuous-filter convolutional neural network for modeling quantum interactions Schutt, Kindermans, Sauceda, Chmiela, Tkatchenko, Muller Jun 2017
SchNet – a deep learning architecture for molecules and materials Schutt, Sauceda, Kindermans, Tkatchenko, Muller Mar 2018
Analysis of Atomistic Representations Using Weighted Skip-Connections Nicoli, Kessel, Gastegger, Schutt Oct 2018
SchNetPack: A Deep Learning Toolbox For Atomistic Systems Schutt, Kessel, Gastegger, Nicoli, Tkatchenko, Muller Nov 2018
Learning representations of molecules and materials with atomistic neural networks Schutt, Tkatchenko, Muller Dec 2018
Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions (SchNOrb) Schutt, Gastegger, Tkatchenko, Muller, Maurer Nov 2019
Combining SchNet and SHARC: The SchNarc Machine Learning Approach for Excited-State Dynamics Westermayr, Gastegger, Marquetand Apr 2020
A deep neural network for molecular wave functions in quasi-atomic minimal basis representation Gastegger, McSloy, Luya, Schutt, Maurer May 2020

Preferred Networks

Title & Link Author(s) Pub. Date
TeaNet: universal neural network interatomic potential inspired by iterative electronic relaxations Takamoto, Izumi, Li Dec 2019
Towards Universal Neural Network Potential for Material Discovery Applicable to Arbitrary Combination of 45 Elements Takamoto, Shinagawa, Motoki, Nakago, Li, Kurata, Watanabe, Yayama, Iriguchi, Asano, Onodera, Ishii, Kudo, Ono, Sawada, Ishitani, Ong, Yamaguchi, Kataoka, Hayashi, Charoenphakdee, Ibuka Jun 2021

Symmetric Gradient Domain Machine Learning (sGDML)

Title & Link Author(s) Pub. Date
Machine learning of accurate energy-conserving molecular force fields Chmiela, Tkatchenko, Sau May 2017
Towards exact molecular dynamics simulations with machine-learned force fields Chmiela, Sauceda, Müller, Tkatchenko Sep 2018
Molecular force fields with gradient-domain machine learning: Construction and application to dynamics of small molecules with coupled cluster forces Sauceda, Chmiela, Poltavsky, Muller, Tkatchenko Feb 2019
sGDML: Constructing accurate and data efficient molecular force fields using machine learning Chmiela, Sauceda, Poltavsky, Muller, Tkatchenko Jul 2019
Construction of Machine Learned Force Fields with Quantum Chemical Accuracy: Applications and Chemical Insights Sauceda, Chmiela, Poltavsky, Muller, Tkatchenko Sep 2019
Accurate Molecular Dynamics Enabled by Efficient Physically-Constrained Machine Learning Approaches Chmiela, Sauceda, Tkatchenko, Muller Dec 2019
Ensemble learning of coarse-grained molecular dynamics force fields with a kernel approach J. Wang, Chmiela, Muller, Noe, Clementi May 2020
Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields Sauceda, Gastegger, Chmiela, Muller, Tkatchenko Sep 2020
Towards Linearly Scaling and Chemically Accurate Global Machine Learning Force Fields for Large Molecules Kabylda, Vassilev-Galindo, Chmiela, Poltavsky, Tkatchenko Sep 2022

DeepPot

Title & Link Author(s) Pub. Date
Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics Zhang, Han, Wang, Car, Weinan Apr 2018
End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems (DeepPot-SE) Zhang, Han, Wang, Saidi, Car, Weinan May 2018
DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models Zhang, Wang, Chen, Zeng, Zhang, Wang, Weinan Oct 2019

DimeNet

Title & Link Author(s) Pub. Date
Directional Message Passing for Molecular Graphs (DimeNet) Gasteiger, Groß, Günnemann Mar 2020
Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules (DimeNet++) Gasteiger, Giri, Margraf, Günnemann Nov 2020

Miscellaneous

Title & Link Author(s) Pub. Date
ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost Smith, Isayev, Roitberg Feb 2017
Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals Chen, Ye, Zuo, Zheng, Ping Ong Dec 2018
Cormorant: Covariant Molecular Neural Networks Anderson, Hy, Kondor Jun 2019
Graph dynamical networks for unsupervised learning of atomic scale dynamics in materials (GDyNets) Xie, France-Lanord, Wang, Shao-Horn, Grossman Jun 2019
Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks (FermiNet) Pfau, Spencer, de G. Matthews, Foulkes Sep 2019
A fast neural network approach for direct covariant forces prediction in complex multi-element extended systems Mailoa, Kornbluth, Batzner, Samsonidze, Lam, Vandermause, Ablitt, Molinari, Kozinsky Sep 2019
SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks Fuchs, Worrall, Fischer, Welling Jun 2020
Equivariant message passing for the prediction of tensorial properties and molecular spectra (PaiNN) Schutt, Unke, Gastegger Feb 2021
ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations Hu, Shuaibi, Das, Goyal, Sriram, Leskovec, Parikh, Zitnick Mar 2021
Accurate and scalable graph neural network force field and molecular dynamics with direct force architecture (GNNFF) Park, Kornbluth, Vandermause, Wolverton, Kozinsky, Mailoa May 2021
Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry (OrbNet-Equi) Qiao, Christensen, Welborn, Manby, Anandkumar, Miller III May 2021
GemNet: Universal Directional Graph Neural Networks for Molecules Gasteiger, Becker, Günnemann Jun 2021
Rotation Invariant Graph Neural Networks using Spin Convolutions (SpinConv) Shuaibi, Kolluru, Das, Grover, Sriram, Ulissi, Zitnick Jun 2021
SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects Unke, Chmiela, Gastegger, Schütt, Sauceda, Müller Dec 2021
Convergence acceleration in machine learning potentials for atomistic simulations Bayerl, Andolina, Dwaraknath, Saidi Jan 2022
NNP/MM: Fast molecular dynamics simulations with machine learning potentials and molecular mechanics Galvelis, Varela-Rial, Doerr, Fino, Eastman, Markland, Chodera, Fabritiis Jan 2022
TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials Tholke, Fabritiis Feb 2022
A Universal Graph Deep Learning Interatomic Potential for the Periodic Table (M3GNet) Chen, Ping Ong Feb 2022
Equivariant Graph Attention Networks for Molecular Property Prediction Le, Noe, Clevert Feb 2022
Learning Atomic Multipoles: Prediction of the Electrostatic Potential with Equivariant Graph Neural Networks Thurlemann, Boselt, Riniker Feb 2022
NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces Haghighatlari, Li, Guan, Zhang, Das, Stein, Zadeh, Liu, M. Head-Gordon, Bertels, Hao, Leven, T. Head-Gordon Feb 2022
MolNet: A Chemically Intuitive Graph Neural Network for Prediction of Molecular Properties Y. Kim, Jeong, J. Kim, E.K. Lee, W.J. Kim, I. Choi Feb 2022
Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids Jørgensen, Bhowmik Aug 2022

Meta-literature

Title & Link Author(s) Pub. Date
Challenges for machine learning force fields in reproducing potential energy surfaces of flexible molecules Vassilev-Galindo, Fonseca, Poltavsky, Tkatchenko Mar 2021
Symmetry Group Equivariant Architectures for Physics Bogatskiy, Ganguly, Kipf, Kondor, Miller, Murnane, Offermann, Pettee, Shanahan, Shimmin, Thais Mar 2022
How Robust are Modern Graph Neural Network Potentials in Long and Hot Molecular Dynamics Simulations? Stocker, Gasteiger, Becker, Gunnemann, Margraf Apr 2022
Forces Are Not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations X. Fu, Z. Wu, W. Wang, T. Xie, Keten, Gomez-Bombarelli, Jaakkola Sep 2022
Neural Scaling of Deep Chemical Models Frey, Soklaski, Alexrod, Samsi, Gomez-Bombarelli, Coley, Gadepally May 2022
Incompleteness of graph neural networks for points clouds in three dimensions Pozdnyakov, Ceriotti Nov 2022