The dark side of the forces: assessing non-conservative force models for atomistic machine learning

Filippo Bigi, Marcel F. Langer, Michele Ceriotti
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:4384-4414, 2025.

Abstract

The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, have 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 non-conservative 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. Contrary to the case of rotational symmetry, energy conservation is hard to learn, monitor, and correct for. The best approach to exploit the acceleration afforded by direct force prediction might be to use it in tandem with a conservative model, reducing – rather than eliminating – the additional cost of backpropagation, but avoiding the pathological behavior associated with non-conservative forces.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-bigi25a, title = {The dark side of the forces: assessing non-conservative force models for atomistic machine learning}, author = {Bigi, Filippo and Langer, Marcel F. and Ceriotti, Michele}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {4384--4414}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/bigi25a/bigi25a.pdf}, url = {https://proceedings.mlr.press/v267/bigi25a.html}, abstract = {The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, have 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 non-conservative 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. Contrary to the case of rotational symmetry, energy conservation is hard to learn, monitor, and correct for. The best approach to exploit the acceleration afforded by direct force prediction might be to use it in tandem with a conservative model, reducing – rather than eliminating – the additional cost of backpropagation, but avoiding the pathological behavior associated with non-conservative forces.} }
Endnote
%0 Conference Paper %T The dark side of the forces: assessing non-conservative force models for atomistic machine learning %A Filippo Bigi %A Marcel F. Langer %A Michele Ceriotti %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-bigi25a %I PMLR %P 4384--4414 %U https://proceedings.mlr.press/v267/bigi25a.html %V 267 %X The use of machine learning to estimate the energy of a group of atoms, and the forces that drive them to more stable configurations, have 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 non-conservative 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. Contrary to the case of rotational symmetry, energy conservation is hard to learn, monitor, and correct for. The best approach to exploit the acceleration afforded by direct force prediction might be to use it in tandem with a conservative model, reducing – rather than eliminating – the additional cost of backpropagation, but avoiding the pathological behavior associated with non-conservative forces.
APA
Bigi, F., Langer, M.F. & Ceriotti, M.. (2025). The dark side of the forces: assessing non-conservative force models for atomistic machine learning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:4384-4414 Available from https://proceedings.mlr.press/v267/bigi25a.html.

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