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Recent studies argue that direct force prediction improves accuracy–efficiency trade-offs and may allow learning energy conservation during training. This work evaluates such nonconservative models in microscopic simulations, revealing fundamental convergence and dynamical instabilities, and recommends combining direct forces with conservative forces for reliable efficiency.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & 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are forces usually computed as derivatives of potential energy in interatomic modeling?","Question",{"text":63,"@type":64},"Because deriving forces from a learned potential energy enforces energy conservation and aligns the model with fundamental physical constraints.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"What issues arise when using non-conservative force prediction models in microscopic simulations?",{"text":68,"@type":64},"The work identifies ill-defined convergence in geometry optimization and instabilities across multiple molecular dynamics settings, making the behavior hard to monitor and correct.",{"name":70,"@type":61,"acceptedAnswer":71},"How does the paper recommend using non-conservative force information safely?",{"text":72,"@type":64},"Use direct force predictions together with conservative forces: pre-train on direct forces and fine-tune via backpropagation, then evaluate with both force types to avoid unphysical effects while retaining most computational efficiency.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},290254,1789641138,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,120,123,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & 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learning  \nFilippo Bigi 1 Marcel F. Langer 1 Michele Ceriotti 1  \nAbstract  \nThe use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, has revolutionized the fields of computational chemistry and materials discovery. In this domain, rigorous enforcement of symmetry and conservation laws has traditionally been considered essential. For this reason, interatomic forces are usually computed as the derivatives of the potential energy, ensuring energy conservation. Several recent works have questioned this physically constrained approach, suggesting that directly predicting the forces yields a better trade-off between accuracy and computational efficiency, and that energy conservation can be learned during training. This work investigates the applicability of such nonconservative models in microscopic simulations. We identify and demonstrate several fundamental issues, from ill-defined convergence of geometry optimization to instability in various types of molecular dynamics. Given the difficulty in monitoring and correcting the lack of energy conservation, direct forces should be used with great care. We show that the best approach to exploit the acceleration they afford is to use them in conjunction with conservative forces. A model can be pre-trained efficiently on direct forces, then fine-tuned using backpropagation. At evaluation time, both force types can be used together to avoid unphysical effects while still benefitting almost entirely from the computational efficiency of direct forces.  \n1Laboratory of Computational Science and Modeling, IMX, ´Ecole Polytechnique Fdrale de Lausanne, 1015 Lausanne, Switzerland. Correspondence to: Michele Ceriotti \u003Cmichele.ceriotti@epfl.ch> .  \nProceedings of the 42 nd International Conference on Machine Learning, Vancouver, Canada. PMLR 267, 2025 . Copyright 2025 by the author(s) .  \n1. Introduction  \nInteratomic potentials model the microscopic interactions between atoms, and determine – directly or by modulating the response to thermal excitations – the stability and reactivity of molecules and materials. Over many decades, interatomic potentials have been used in Monte Carlo (Metropolis et al., 1953) and molecular dynamics (MD) (Andersen, 1980) simulations, geometry optimization, and other techniques, allowing a mechanistic study of the atomic-scale behavior and properties of molecules, materials, and biological systems (Allen & Tildesley, 2017 ; Tuckerman, 2008) . While traditional interatomic potentials are based on simple physically inspired functional forms, the last decade has seen machine-learned interatomic potentials (MLIPs) obtain remarkable accuracies at a high level of computational efficiency, most often by learning reference energies and forces from much slower first-principle quantum mechanical calculations (Behler, 2021 ; Unke et al., 2021) .  \nAt first, such machine-learned interatomic potentials were trained on quantum mechanical data specific to the chemical system of interest. Over the last years, more diverse datasets have emerged, consisting of up to billions of targets, and spanning much of the periodic table (Chanussot et al., 2021 ; Tran et al., 2023 ; Barroso-Luque et al., 2024 ; Schmidt et al., 2024) . This has not only led to an increase in the complexity of the models, going from linear or kernel regression to deep graph neural networks, but it has also pushed many recent models to abandon some of the underlying physical symmetries of interatomic potentials in favor of simpler – and potentially more scalable and efficient – architectures (Pozdnyakov & Ceriotti, 2023 ; Neumann et al., 2024 ; Qu & Krishnapriyan, 2024) . In such models, symmetries are learned from data, aided by data augmentation.  \nSome recent models for interatomic potentials also disregard the property of energy conservation (Gas","cbCaik2A4nbrWmrA","https://ap.wps.com/l/cbCaik2A4nbrWmrA","pdf",1400079,31,"English","# Abstract\n# 1. Introduction\n# 2. Background and related work\n## 2.1. Interatomic potentials and atomistic simulations","[{\"question\":\"Why are forces usually computed as derivatives of potential energy in interatomic modeling?\",\"answer\":\"Because deriving forces from a learned potential energy enforces energy conservation and aligns the model with fundamental physical constraints.\"},{\"question\":\"What issues arise when using non-conservative force prediction models in microscopic simulations?\",\"answer\":\"The work identifies ill-defined convergence in geometry optimization and instabilities across multiple molecular dynamics settings, making the behavior hard to monitor and correct.\"},{\"question\":\"How does the paper recommend using non-conservative force information safely?\",\"answer\":\"Use direct force predictions together with conservative forces: pre-train on direct forces and fine-tune via backpropagation, then evaluate with both force types to avoid unphysical effects while retaining most computational efficiency.\"}]","The dark side of the forces - Assessing non-conservative force models for atomistic machine learning | PDF",78]