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An overview of literature that discusses the use of machine learning for atomistic simulations
https://github.com/m-k-S/awesome-machine-learning-atomistic-simulation

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An overview of literature that discusses the use of machine learning for atomistic simulations

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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](#embeddings-and-representations)

    - [Atomic Cluster Expansion (ACE)](#atomic-cluster-expansion-ace)

    - [Smooth Overlap of Atomic Position (SOAP)](#smooth-overlap-of-atomic-position-soap)

    - [Gaussian Approximation Potentials (GAP)](#gaussian-approximation-potentials-gap)

    - [Moment Tensor Potentials (MTP)](#moment-tensor-potentials-mtp)

    - [Atom-Centered Symmetry Functions (ACSF)](#atom-centered-symmetry-functions-acsf)

    - [FCHL](#fchl)

    - [Wavelet Scattering](#wavelet-scattering)

    - [Miscellaneous](#miscellaneous)

    - [Meta-literature](#meta-literature)

  - [Tools and Architectures](#tools-and-architectures)

    - [e3nn Precursor](#e3nn-precursor)

    - [e3nn](#e3nn)

    - [Equivariant Graph Neural Networks (EGNN)](#equivariant-graph-neural-networks-egnn)

    - [SchNet](#schnet)

    - [Preferred Networks](#preferred-networks)

    - [Symmetric Gradient Domain Machine Learning (sGDML)](#symmetric-gradient-domain-machine-learning-sgdml)

    - [DeepPot](#deeppot)

    - [DimeNet](#dimenet)

    - [Miscellaneous](#miscellaneous)

    - [Meta-literature](#meta-literature)



## 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](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.99.014104) | Drautz | Jan 2019 |

| [Atomic cluster expansion of scalar, vectorial and tensorial properties and including magnetism and charge transfer](https://arxiv.org/abs/2003.00221) | Drautz | Feb 2020 |

| [Performant implementation of the atomic cluster expansion: Application to copper and silicon](https://arxiv.org/abs/2103.00814) | Lysogorskiy, van der Oord, Bochkarev, Menon, Rinaldi, Hammerschmidt, Mrovec, Thompson, Csányi, Ortner, Drautz | Mar 2021 |

| [Efficient parametrization of the atomic cluster expansion](https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.6.013804) | Bochkarev, Lysogorskiy, Menon, Qamar, Mrovec, Drautz | Jan 2022 |

| [Atomic cluster expansion: Completeness, efficiency and stability](https://www.sciencedirect.com/science/article/pii/S0021999122000080?via%3Dihub) | Dusson, Bachmayr, Csanyi, Drautz, Etter, van der Oord, Ortner | Apr 2022 |

| [Multilayer atomic cluster expansion for semi-local interactions](https://arxiv.org/pdf/2205.08177.pdf) | Bochkarev, Lysogorskiy, Ortner, Csanyi, Drautz | May 2022 |

| [Atomic cluster expansion and wave function representations](https://arxiv.org/abs/2206.11375) | Drautz, Ortner | Jun 2022 |

| [Permutation-adapted complete and independent basis for atomic cluster expansion descriptors](https://arxiv.org/abs/2208.01756) | Goff, Sievers, Wood, Thompson | Aug 2022 |



### Smooth Overlap of Atomic Position (SOAP)



| Title & Link | Author(s) | Pub. Date |

| ------------ | --------- | --------- |

| [On representing chemical environments](https://arxiv.org/abs/1209.3140) | Bartok, Kondor, Csanyi | Mar 2013 |

| [Comparing molecules and solids across structural and alchemical space](https://pubs.rsc.org/en/content/articlelanding/2016/cp/c6cp00415f) | De, Bartok, Csanyi, Ceriotti | Apr 2016 |

| [Automatic Selection of Atomic Fingerprints and Reference Configurations for Machine-Learning Potentials](https://arxiv.org/abs/1804.02150) | Imbalzano, Anelli, Giofré, Klees, Behler, Ceriotti | Apr 2018 |

| [Machine-learning of atomic-scale properties based on physical principles](https://arxiv.org/abs/1901.10971) | Ceriotti, Willatt, Csányi | Jan 2019 |

| [Atom-density representations for machine learning](https://aip.scitation.org/doi/10.1063/1.5090481) | Willatt, Musil, Ceriotti | Apr 2019 |

| [Atomic-scale representation and statistical learning of tensorial properties](https://arxiv.org/abs/1904.01623) | Grisafi, Wilkins, Willatt, Ceriotti | Apr 2019 |

| [Optimizing many-body atomic descriptors for enhanced computational performance of machine learning based interatomic potentials](https://arxiv.org/abs/1905.02142) | Caro | May 2019 |

| [Efficient implementation of atom-density representations](https://arxiv.org/abs/2101.08814) | Musil, Veit, Goscinski, Fraux, Willatt, Stricker, Junge, Ceriotti | Jan 2021 |



### Gaussian Approximation Potentials (GAP)

(Many applications paper omitted; please [see here](https://arxiv.org/search/?query=%22Gaussian+Approximation+Potential%22&searchtype=all&source=header) for a more comprehensive list)



| Title & Link | Author(s) | Pub. Date |

| ------------ | --------- | --------- |

| [Gaussian Approximation Potentials: the accuracy of quantum mechanics, without the electrons](https://arxiv.org/abs/0910.1019) | Bartok, Payne, Kondor, Csanyi | Oct 2009 |

| [Gaussian Approximation Potential: an interatomic potential derived from first principles Quantum Mechanics](https://arxiv.org/abs/1003.2817) | Bartok | Mar 2010 |

| [Accuracy and transferability of GAP models for tungsten](https://arxiv.org/abs/1405.4370) | Szlachta, Bartok, Csanyi | May 2014 |

| [Localized Coulomb Descriptors for the Gaussian Approximation Potential](https://arxiv.org/abs/1611.05126) | Barker, Bulin, Hamaekers, Mathias | Nov 2016 |

| [Many-Body Coarse-Grained Interactions using Gaussian Approximation Potentials](https://arxiv.org/abs/1611.09123) | John | Nov 2016 |

| [Machine-learned Interatomic Potentials for Alloys and Alloy Phase Diagrams](https://arxiv.org/abs/1906.07816) | Rosenbrock, Gubaev, Shapeev, Pártay, Bernstein, Csányi, Hart | Jun 2019 |

| [Combining phonon accuracy with high transferability in Gaussian approximation potential models](https://arxiv.org/abs/2005.07046) | George, Hautier, Bartok, Csanyi, Deringer | May 2020 |

| [Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials](https://pubs.acs.org/doi/10.1021/acs.jctc.0c00347) | Zaverkin, Kastner | July 2020 |

| [Massively Parallel Fitting of Gaussian Approximation Potentials](https://arxiv.org/abs/2207.03803) | Klawohn, Kermode, Bartók | Jul 2022 |

| [Atomistic structure search using local surrogate mode](https://arxiv.org/abs/2208.09273) | 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](https://arxiv.org/abs/1512.06054) | Shapeev | Dec 2015 |

| [Moment tensor Potentials as a Promising Tool to Study Diffusion Processes](https://arxiv.org/abs/1812.02946) | Novoselov, Yanilkin, Shapeev, Podryabinkin | Dec 2018 |

| [Machine-learning potentials enable predictive and tractable high-throughput screening of random alloys](https://arxiv.org/abs/2107.05620) | 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](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.98.146401) | Behler, Parrinello | Apr 2007 |

| [Atom-centered symmetry functions for constructing high-dimensional neural network potentials](https://aip.scitation.org/doi/abs/10.1063/1.3553717) | Behler | Feb 2011 |

| [An implementation of artificial neural-network potentials for atomistic materials simulations: Performance for TiO2](https://www.sciencedirect.com/science/article/abs/pii/S0927025615007806?via%3Dihub)  (aenet) | Artrith, Urban | Mar 2016 |

| [Amp: A modular approach to machine learning in atomistic simulations](https://www.sciencedirect.com/science/article/abs/pii/S0010465516301266?via%3Dihub) | Khorshidi, Peterson | Oct 2016 |

| [Efficient and accurate machine-learning interpolation of atomic energies in compositions with many species](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.96.014112) | Artrith, Urban, Ceder | Jul 2017 |

| [wACSF—Weighted atom-centered symmetry functions as descriptors in machine learning potentials](https://aip.scitation.org/doi/10.1063/1.5019667) | Gastegger, Schwiedrzik, Bittermann, Berzsenyi, Marquetand | Mar 2018 |

| [Optimized symmetry functions for machine-learning interatomic potentials of multicomponent systems](https://aip.scitation.org/doi/10.1063/1.5040005) | Rostami, Amsler, Ghasemi | Sep 2018 |

| [Augmenting machine learning of energy landscapes with local structural information](https://aip.scitation.org/doi/10.1063/5.0012407) | Honrao, Xie, Hennig | Aug 2020 |

| [A fourth-generation high-dimensional neural network potential with accurate electrostatics including non-local charge transfer](https://www.nature.com/articles/s41467-020-20427-2) | Wai Ko, Finkler, Goedecker, Behler | Jan 2021 |

| [Unified theory of atom-centered representations and message-passing machine-learning schemes](https://aip.scitation.org/doi/pdf/10.1063/5.0087042) | 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](https://aip.scitation.org/doi/10.1063/1.5020710) | Faber, Christensen, Huang, von Lilienfeld | Mar 2018 |

| [FCHL revisited: Faster and more accurate quantum machine learning](https://aip.scitation.org/doi/10.1063/1.5126701) | Christensen, Bratholm, Faber, von Lilienfeld | Jan 2020 |



### Wavelet Scattering



| Title & Link | Author(s) | Pub. Date |

| ------------ | --------- | --------- |

| [Solid harmonic wavelet scattering](https://dl.acm.org/doi/10.5555/3295222.3295400) | Eickenberg, Exarchakis, Hirn, Mallat | Dec 2017 |

| [Steerable Wavelet Scattering for 3D Atomic Systems with Application to Li-Si Energy Prediction](https://arxiv.org/abs/1812.02320) | Brumwell, Sinz, Jin Kim, Qi, Hirn | Nov 2018 |

| [Wavelet Scattering Networks for Atomistic Systems with Extrapolation of Material Properties](https://arxiv.org/abs/2006.01247) | 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](https://aip.scitation.org/doi/10.1063/1.3095491) | 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](https://onlinelibrary.wiley.com/doi/abs/10.1002/qua.24912) | von Lilienfeld, Ramakrishnan, Rupp, Knoll | Jul 2013 |

| [How to represent crystal structures for machine learning: Towards fast prediction of electronic properties](https://journals.aps.org/prb/abstract/10.1103/PhysRevB.89.205118) | Schutt, Glawe, Brockherde, Sanna, Muller, Gross | May 2014 |

| [A fingerprint based metric for measuring similarities of crystalline structures](https://aip.scitation.org/doi/10.1063/1.4940026) | Zhu, Amsler, Fuhrer, Schaefer, Faraji, Rostami, Ghasemi, Sadeghi, Grauzinyte, Wolverton, Goedecker | Jan 2016 |

| [Unified Representation of Molecules and Crystals for Machine Learning](https://arxiv.org/abs/1704.06439) (MBTR) | Huo, Rupp | Apr 2017 |

| [An Atomistic Fingerprint Algorithm for Learning Ab Initio Molecular Force Fields](https://arxiv.org/abs/1709.09235) | Tang, Zhang, Karniadakis | Dec 2017 |

| [A novel approach to describe chemical environments in high-dimensional neural network potentials](https://aip.scitation.org/doi/10.1063/1.5086167) | Kocer, Mason, Erturk | Mar 2019 |

| [Embedded Atom Neural Network Potentials: Efficient and Accurate Machine Learning with a Physically Inspired Representation](https://pubs.acs.org/doi/abs/10.1021/acs.jpclett.9b02037) (EAM) | Zhang, Hu, Jiang | Aug 2019 |

| [Continuous and optimally complete description of chemical environments using Spherical Bessel descriptors](https://aip.scitation.org/doi/10.1063/1.5111045) (SB) | Kocer, Mason, Erturk | Jan 2020 |

| [TUCAN: A molecular identifier and descriptor applicable to the whole periodic table from hydrogen to oganesson](https://europepmc.org/article/ppr/ppr479842) | 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](https://journals.aps.org/prmaterials/abstract/10.1103/PhysRevMaterials.2.083802) | Ouyang, Curtarolo, Ahmetcik, Scheffler, Ghiringhelli | Aug 2018 |

| [A Performance and Cost Assessment of Machine Learning Interatomic Potentials](https://arxiv.org/abs/1906.08888) | Zuo, Chen, Li, Deng, Chen, Behler, Csányi, Shapeev, Thompson, Wood, Ong | Jul 2019 |

| [DScribe: Library of descriptors for machine learning in materials science](https://www.sciencedirect.com/science/article/pii/S0010465519303042) | 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](https://aip.scitation.org/doi/10.1063/5.0009491) | Jinnouchi, Karsai, Verdi, Asahi, Kresse | Apr 2020 |

| [Sensitivity and Dimensionality of Atomic Environment Representations used for Machine Learning Interatomic Potentials](https://arxiv.org/abs/2006.01915) | Onat, Ortner, Kermode | Jun 2020 |

| [An assessment of the structural resolution of various fingerprints commonly used in machine learning](https://arxiv.org/abs/2008.03189) | Karamad, Magar, Shi, Siahrostami, Gates, Farimani | Aug 2020 |

| [Incompleteness of Atomic Structure Representations](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.166001) | 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](https://arxiv.org/abs/2102.06915) | Parsaeifard, Goedecker | Feb 2021 |

| [The role of feature space in atomistic learning](https://iopscience.iop.org/article/10.1088/2632-2153/abdaf7) | Goscinski, Fraux, Imbalzano, Ceriotti | Apr 2021 |

| [Strategies for the Construction of Machine-Learning Potentials for Accurate and Efficient Atomic-Scale Simulations](https://arxiv.org/pdf/2101.10468.pdf) | Miksch, Morawietz, Kästner, Urban, Artrith | May 2021 |

| [Compressing local atomic neighbourhood descriptors](https://arxiv.org/abs/2112.13055) | 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](https://www.youtube.com/watch?v=8CF8Grb_brE&t=1224s) into the [e3nn](https://e3nn.org/) framework.



| Title & Link | Author(s) | Pub. Date |

| ------------ | --------- | --------- |

| [Group Equivariant Convolutional Networks](https://arxiv.org/abs/1602.07576) | Cohen, Welling | Feb 2016 |

| [Spherical CNNs](https://arxiv.org/abs/1801.10130) | Cohen, Geiger, Koehler, Welling | Jan 2018 |

| [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://arxiv.org/abs/1802.08219) | Smidt, Thomas, Kearnes, Yang, Li, Kohlhoff, Riley | Feb 2018 |

| [N-body Networks: a Covariant Hierarchical Neural Network Architecture for Learning Atomic Potentials](https://arxiv.org/abs/1803.01588) | Kondor | Mar 2018 |

| [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://arxiv.org/abs/1806.09231) | Kondor, Lin, Trivedi | Jun 2018 |

| [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://arxiv.org/abs/1807.02547) | Weiler, Geiger, Welling, Boomsma, Cohen | Jul 2018 |

| [SE(3)-Equivariant prediction of molecular wavefunctions and electronic densities](https://arxiv.org/abs/2106.02347) | Unke, Bogojeski, Gastegger, Geiger, Smidt, Müller | Jun 2021 |



### e3nn

| Title & Link | Author(s) | Pub. Date |

| ------------ | --------- | --------- |

| [Finding symmetry breaking order parameters with Euclidean neural networks](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.3.L012002) | Smidt, Geiger, Miller | Jul 2020 |

| [Relevance of Rotationally Equivariant Convolutions for Predicting Molecular Properties](https://arxiv.org/abs/2008.08461) | Miller, Geiger, Smidt, Noe | Aug 2020 |

| [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://arxiv.org/abs/2101.03164) (NequIP) | Batzner, Musaelian, Sun, Geiger, Mailoa, Kornbluth, Molinari, Smidt, Kozinsky | Jan 2021]

| [Direct Prediction of Phonon Density of States With Euclidean Neural Networks](https://onlinelibrary.wiley.com/doi/full/10.1002/advs.202004214) | 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](https://arxiv.org/abs/2201.03726) | Rackers, Tecot, Geiger, Smidt | Jan 2022 |

| [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://arxiv.org/pdf/2204.05249.pdf) (Allegro) | Musaelian, Batzner, Johansson, Sun, Owen, Kornbluth, Kozinsky | Apr 2022 |

| [The Design Space of E(3)-Equivariant Atom-Centered Interatomic Potentials](https://arxiv.org/abs/2205.06643) (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](https://arxiv.org/abs/2206.07697) | Batatia, Kovács, Simm, Ortner, Csányi | Jun 2022 |

| [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://arxiv.org/abs/2206.11990) | Liao, Smidt | Jun 2022 |

| [e3nn: Euclidean Neural Networks](https://arxiv.org/abs/2207.09453) | Geiger, Smidt | Jul 2022 |

| [Machine Learning Magnetism Classifiers from Atomic Coordinates](https://www.sciencedirect.com/science/article/pii/S258900422201464X) | 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](https://arxiv.org/abs/2304.03694) | Rensmeyer, Craig, Kramer, Niggemann | Apr 2023 |



### Equivariant Graph Neural Networks (EGNN)

| Title & Link | Author(s) | Pub. Date |

| ------------ | --------- | --------- |

| [E(n)-Equivariant Graph Neural Networks](https://arxiv.org/abs/2102.09844) | Satorras, Hoogeboom, Welling | Feb 2021 |

| [E(n)-Equivariant Normalizing Flows](https://arxiv.org/abs/2105.09016) | Satorras, Hoogeboom, Fuchs, Posner, Welling | May 2021 |

| [Geometric and Physical Quantities Improve E(3)-Equivariant Message Passing](https://arxiv.org/abs/2110.02905) (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](https://arxiv.org/abs/1706.08566) | Schutt, Kindermans, Sauceda, Chmiela, Tkatchenko, Muller | Jun 2017 |

| [SchNet – a deep learning architecture for molecules and materials](https://arxiv.org/pdf/1712.06113.pdf) | Schutt, Sauceda, Kindermans, Tkatchenko, Muller | Mar 2018 |

| [Analysis of Atomistic Representations Using Weighted Skip-Connections](https://arxiv.org/abs/1810.09751) | Nicoli, Kessel, Gastegger, Schutt | Oct 2018 |

| [SchNetPack: A Deep Learning Toolbox For Atomistic Systems](https://pubs.acs.org/doi/10.1021/acs.jctc.8b00908) | Schutt, Kessel, Gastegger, Nicoli, Tkatchenko, Muller | Nov 2018 |

| [Learning representations of molecules and materials with atomistic neural networks](https://arxiv.org/abs/1812.04690) | Schutt, Tkatchenko, Muller | Dec 2018 |

| [Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions](https://www.nature.com/articles/s41467-019-12875-2) (SchNOrb) | Schutt, Gastegger, Tkatchenko, Muller, Maurer | Nov 2019 |

| [Combining SchNet and SHARC: The SchNarc Machine Learning Approach for Excited-State Dynamics](https://pubs.acs.org/doi/full/10.1021/acs.jpclett.0c00527) | Westermayr, Gastegger, Marquetand | Apr 2020 |

| [A deep neural network for molecular wave functions in quasi-atomic minimal basis representation](https://arxiv.org/abs/2005.06979) | 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](https://arxiv.org/abs/1912.01398) | Takamoto, Izumi, Li | Dec 2019 |

| [Towards Universal Neural Network Potential for Material Discovery Applicable to Arbitrary Combination of 45 Elements](https://arxiv.org/pdf/2106.14583.pdf) | 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](https://www.science.org/doi/10.1126/sciadv.1603015) | Chmiela, Tkatchenko, Sau | May 2017 |

| [Towards exact molecular dynamics simulations with machine-learned force fields](https://www.nature.com/articles/s41467-018-06169-2) | 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](https://aip.scitation.org/doi/10.1063/1.5078687) | Sauceda, Chmiela, Poltavsky, Muller, Tkatchenko | Feb 2019 |

| [sGDML: Constructing accurate and data efficient molecular force fields using machine learning](https://www.sciencedirect.com/science/article/pii/S0010465519300591?via%3Dihub) | Chmiela, Sauceda, Poltavsky, Muller, Tkatchenko | Jul 2019 |

| [Construction of Machine Learned Force Fields with Quantum Chemical Accuracy: Applications and Chemical Insights](https://arxiv.org/abs/1909.08565) | Sauceda, Chmiela, Poltavsky, Muller, Tkatchenko | Sep 2019 |

| [Accurate Molecular Dynamics Enabled by Efficient Physically-Constrained Machine Learning Approaches](https://arxiv.org/abs/1912.06401) | Chmiela, Sauceda, Tkatchenko, Muller | Dec 2019 |

| [Ensemble learning of coarse-grained molecular dynamics force fields with a kernel approach](https://aip.scitation.org/doi/10.1063/5.0007276) | J. Wang, Chmiela, Muller, Noe, Clementi | May 2020 |

| [Molecular force fields with gradient-domain machine learning (GDML): Comparison and synergies with classical force fields](https://aip.scitation.org/doi/10.1063/5.0023005) | Sauceda, Gastegger, Chmiela, Muller, Tkatchenko | Sep 2020 |

| [Towards Linearly Scaling and Chemically Accurate Global Machine Learning Force Fields for Large Molecules](https://arxiv.org/abs/2209.03985) | 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](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.120.143001) | Zhang, Han, Wang, Car, Weinan | Apr 2018 |

| [End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems](https://arxiv.org/abs/1805.09003) (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](https://arxiv.org/abs/1910.12690) | Zhang, Wang, Chen, Zeng, Zhang, Wang, Weinan | Oct 2019 |



### DimeNet

| Title & Link | Author(s) | Pub. Date |

| ------------ | --------- | --------- |

| [Directional Message Passing for Molecular Graphs](https://arxiv.org/abs/2003.03123) (DimeNet) | Gasteiger, Groß, Günnemann | Mar 2020 |

| [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://arxiv.org/abs/2011.14115) (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](https://pubs.rsc.org/en/content/articlelanding/2017/SC/C6SC05720A) | Smith, Isayev, Roitberg | Feb 2017 |

| [Graph Networks as a Universal Machine Learning Framework for Molecules and Crystals](https://arxiv.org/abs/1812.05055) | Chen, Ye, Zuo, Zheng, Ping Ong | Dec 2018 |

| [Cormorant: Covariant Molecular Neural Networks](https://arxiv.org/abs/1906.04015) | Anderson, Hy, Kondor | Jun 2019 |

| [Graph dynamical networks for unsupervised learning of atomic scale dynamics in materials](https://www.nature.com/articles/s41467-019-10663-6) (GDyNets) | Xie, France-Lanord, Wang, Shao-Horn, Grossman | Jun 2019 |

| [Ab-Initio Solution of the Many-Electron Schrödinger Equation with Deep Neural Networks](https://arxiv.org/abs/1909.02487) (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](https://www.nature.com/articles/s42256-019-0098-0) | Mailoa, Kornbluth, Batzner, Samsonidze, Lam, Vandermause, Ablitt, Molinari, Kozinsky | Sep 2019 |

| [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://arxiv.org/abs/2006.10503) | Fuchs, Worrall, Fischer, Welling | Jun 2020 |

| [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://arxiv.org/abs/2102.03150) (PaiNN) | Schutt, Unke, Gastegger | Feb 2021 |

| [ForceNet: A Graph Neural Network for Large-Scale Quantum Calculations](https://arxiv.org/abs/2103.01436) | 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](https://www.nature.com/articles/s41524-021-00543-3) (GNNFF) | Park, Kornbluth, Vandermause, Wolverton, Kozinsky, Mailoa | May 2021 |

| [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://arxiv.org/pdf/2105.14655.pdf) (OrbNet-Equi) | Qiao, Christensen, Welborn, Manby, Anandkumar, Miller III | May 2021 |

| [GemNet: Universal Directional Graph Neural Networks for Molecules](https://arxiv.org/pdf/2106.08903.pdf) | Gasteiger, Becker, Günnemann | Jun 2021 |

| [Rotation Invariant Graph Neural Networks using Spin Convolutions](https://arxiv.org/abs/2106.09575) (SpinConv) | Shuaibi, Kolluru, Das, Grover, Sriram, Ulissi, Zitnick | Jun 2021 |

| [SpookyNet: Learning force fields with electronic degrees of freedom and nonlocal effects](https://www.nature.com/articles/s41467-021-27504-0#Abs1) | Unke, Chmiela, Gastegger, Schütt, Sauceda, Müller | Dec 2021 |

| [Convergence acceleration in machine learning potentials for atomistic simulations](https://pubs.rsc.org/en/content/articlehtml/2022/dd/d1dd00005e) | Bayerl, Andolina, Dwaraknath, Saidi | Jan 2022 |

| [NNP/MM: Fast molecular dynamics simulations with machine learning potentials and molecular mechanics](https://arxiv.org/abs/2201.08110) | Galvelis, Varela-Rial, Doerr, Fino, Eastman, Markland, Chodera, Fabritiis | Jan 2022 |

| [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://arxiv.org/abs/2202.02541) | Tholke, Fabritiis | Feb 2022 |

| [A Universal Graph Deep Learning Interatomic Potential for the Periodic Table](https://arxiv.org/abs/2202.02450) (M3GNet) | Chen, Ping Ong | Feb 2022 |

| [Equivariant Graph Attention Networks for Molecular Property Prediction](https://arxiv.org/abs/2202.09891) | Le, Noe, Clevert | Feb 2022 |

| [Learning Atomic Multipoles: Prediction of the Electrostatic Potential with Equivariant Graph Neural Networks](https://pubs.acs.org/doi/10.1021/acs.jctc.1c01021) | Thurlemann, Boselt, Riniker | Feb 2022 |

| [NewtonNet: a Newtonian message passing network for deep learning of interatomic potentials and forces](https://pubs.rsc.org/en/content/articlehtml/2022/dd/d2dd00008c) | 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](https://arxiv.org/abs/2203.09456) | 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](https://www.nature.com/articles/s41524-022-00863-y) | 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](https://aip.scitation.org/doi/10.1063/5.0038516) | Vassilev-Galindo, Fonseca, Poltavsky, Tkatchenko | Mar 2021 |

| [Symmetry Group Equivariant Architectures for Physics](https://arxiv.org/abs/2203.06153) | 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?](https://chemrxiv.org/engage/chemrxiv/article-details/6246035d3affe4aa143c3848) | Stocker, Gasteiger, Becker, Gunnemann, Margraf | Apr 2022 |

| [Forces Are Not Enough: Benchmark and Critical Evaluation for Machine Learning Force Fields with Molecular Simulations](https://arxiv.org/abs/2210.07237) | X. Fu, Z. Wu, W. Wang, T. Xie, Keten, Gomez-Bombarelli, Jaakkola | Sep 2022 |

| [Neural Scaling of Deep Chemical Models](https://chemrxiv.org/engage/chemrxiv/article-details/627bddd544bdd532395fb4b5) | Frey, Soklaski, Alexrod, Samsi, Gomez-Bombarelli, Coley, Gadepally | May 2022 |

| [Incompleteness of graph neural networks for points clouds in three dimensions](https://iopscience.iop.org/article/10.1088/2632-2153/aca1f8) | Pozdnyakov, Ceriotti | Nov 2022 |