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1. A practical guide to machine learning interatomic potentials – Status and future

   https://doi.org/10.1016/j.cossms.2025.101214  

   Jacobs, Ryan; Morgan, Dane; Attarian, Siamak; Meng, Jun; Shen, Chen; Wu, Zhenghao; Xie, Clare Yijia; Yang, Julia H; Artrith, Nongnuch; Blaiszik, Ben; et al (March 2025, Current Opinion in Solid State and Materials Science)

   The rapid development and large body of literature on machine learning interatomic potentials (MLIPs) can make it difficult to know how to proceed for researchers who are not experts but wish to use these tools. The spirit of this review is to help such researchers by serving as a practical, accessible guide to the state-of-the-art in MLIPs. This review paper covers a broad range of topics related to MLIPs, including (i) central aspects of how and why MLIPs are enablers of many exciting advancements in molecular modeling, (ii) the main underpinnings of different types of MLIPs, including their basic structure and formalism, (iii) the potentially transformative impact of universal MLIPs for both organic and inorganic systems, including an overview of the most recent advances, capabilities, downsides, and potential applications of this nascent class of MLIPs, (iv) a practical guide for estimating and understanding the execution speed of MLIPs, including guidance for users based on hardware availability, type of MLIP used, and prospective simulation size and time, (v) a manual for what MLIP a user should choose for a given application by considering hardware resources, speed requirements, energy and force accuracy requirements, as well as guidance for choosing pre-trained potentials or fitting a new potential from scratch, (vi) discussion around MLIP infrastructure, including sources of training data, pre-trained potentials, and hardware resources for training, (vii) summary of some key limitations of present MLIPs and current approaches to mitigate such limitations, including methods of including long-range interactions, handling magnetic systems, and treatment of excited states, and finally (viii) we finish with some more speculative thoughts on what the future holds for the development and application of MLIPs over the next 3–10+ years. 

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2. How neural networks extrapolate: from feedforward to graph neural networks

   Xu, Keyulu; Zhang, Mozhi; Li, Jingling; Du, Simon S.; Kawarabayashi, Ken-ichi; Jegelka, Stefanie (January 2021, International Conference on Learning Representations (ICLR))

   null (Ed.)

   We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) – structured networks with MLP modules – have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify the observation that ReLU MLPs quickly converge to linear functions along any direction from the origin, which implies that ReLU MLPs do not extrapolate most nonlinear functions. But, they can provably learn a linear target function when the training distribution is sufficiently “diverse”. Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e.g., larger graphs or edge weights) relies on encoding task-specific non-linearities in the architecture or features. Our theoretical analysis builds on a connection of over-parameterized networks to the neural tangent kernel. Empirically, our theory holds across different training settings. 

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3. How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks

   Xu, K.; Zhang, M; Li, J; Du, S.; Kawarabayashi, K; Jegelka, S. (January 2021, International Conference on Learning Representations (ICLR))

   We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) – structured networks with MLP modules – have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify the observation that ReLU MLPs quickly converge to linear functions along any direction from the origin, which implies that ReLU MLPs do not extrapolate most nonlinear functions. But, they can provably learn a linear target function when the training distribution is sufficiently “diverse”. Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e.g., larger graphs or edge weights) relies on encoding task-specific non-linearities in the architecture or features. Our theoretical analysis builds on a connection of over-parameterized networks to the neural tangent kernel. Empirically, our theory holds across different training settings. 

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4. Convergence acceleration in machine learning potentials for atomistic simulations

   https://doi.org/10.1039/D1DD00005E  

   Bayerl, Dylan; Andolina, Christopher M.; Dwaraknath, Shyam; Saidi, Wissam A. (February 2022, Digital Discovery)

   Machine learning potentials (MLPs) for atomistic simulations have an enormous prospective impact on materials modeling, offering orders of magnitude speedup over density functional theory (DFT) calculations without appreciably sacrificing accuracy in the prediction of material properties. However, the generation of large datasets needed for training MLPs is daunting. Herein, we show that MLP-based material property predictions converge faster with respect to precision for Brillouin zone integrations than DFT-based property predictions. We demonstrate that this phenomenon is robust across material properties for different metallic systems. Further, we provide statistical error metrics to accurately determine a priori the precision level required of DFT training datasets for MLPs to ensure accelerated convergence of material property predictions, thus significantly reducing the computational expense of MLP development. 

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5. PyXtal_FF: a python library for automated force field generation

   https://doi.org/10.1088/2632-2153/abc940  

   Yanxon, Howard; Zagaceta, David; Tang, Binh; Matteson, David S.; Zhu, Qiang (December 2020, Machine Learning: Science and Technology)

   Abstract We present PyXtal_FF—a package based on Python programming language—for developing machine learning potentials (MLPs). The aim of PyXtal_FF is to promote the application of atomistic simulations through providing several choices of atom-centered descriptors and machine learning regressions in one platform. Based on the given choice of descriptors (including the atom-centered symmetry functions, embedded atom density, SO4 bispectrum, and smooth SO3 power spectrum), PyXtal_FF can train MLPs with either generalized linear regression or neural network models, by simultaneously minimizing the errors of energy/forces/stress tensors in comparison with the data fromab-initiosimulations. The trained MLP model from PyXtal_FF is interfaced with the Atomic Simulation Environment (ASE) package, which allows different types of light-weight simulations such as geometry optimization, molecular dynamics simulation, and physical properties prediction. Finally, we will illustrate the performance of PyXtal_FF by applying it to investigate several material systems, including the bulk SiO₂, high entropy alloy NbMoTaW, and elemental Pt for general purposes. Full documentation of PyXtal_FF is available athttps://pyxtal-ff.readthedocs.io. 

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