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

TL;DR

The work critically evaluates non-conservative force predictions in atomistic ML interatomic potentials, demonstrating that direct force models can destabilize geometry optimization and MD due to broken energy conservation. It introduces quantitative diagnostics (Jacobian symmetry and the lambda metric) and shows that thermostats and non-physical dynamics can confound simulations, sometimes catastrophically. The authors advocate a hybrid approach: pretrain on direct forces for speed, then fine-tune to enforce energy conservation, and use multiple-time-stepping to combine fast non-conservative predictions with accurate conservative corrections. This yields practical, scalable strategies for deploying universal ML interatomic potentials while maintaining physically meaningful simulations.

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, 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 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. 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.

Figures (18)

• Figure 1: Comparison of the norm of each block of the Jacobian, $\mathbf{J}_{ij}$, and of its antisymmetric component, for different pairs of atoms, as a function of their distance $r_{ij}$, computed for a randomly selected bulk water structure from the test set.
• Figure 2: Time series for the kinetic temperature along a NVE MD trajectory, for ORB, the conservative and non-conservative PET models, and for a PET-M model using a multiple time-stepping (MTS) algorithm that evaluates conservative forces every 8 steps.
• Figure 3: Velocity power spectrum $\hat{c}_{vv}(\omega)$, for different PET models and thermostat types: A conservative (C) and non-conservative (NC) model using white-noise Langevin (WN) and stochastic velocity rescaling (SVR) thermostats.
• Figure 4: Training curves for PET-C and PET-NC models, and the conservative fine-tuning of a hybrid PET-M model initialized (epoch marked with arrow) from the potential energy head of the PET-NC model.
• Figure 5: A schematic representation of the interactions in a (ML) interatomic potential. (a) Contributions to an $i$-centered prediction of energy or force from three or more neighbors, labeled $j$ and $k$. (b) Contributions from a $j$-centered energy prediction to the force on the $i$-th atom, computed by back-propagation.