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

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.

Computer simulations are an important part of the search for high-performance materials and the development of pharmaceuticals. Unfortunately, these simulations are very expensive since they involve numerically solving physical equations to high precision. To lower this cost, machine learning models can be trained on example calculations to predict their outcome much more efficiently.There is a lot of debate about how to design and improve these surrogate models, particularly around the question to what extent the models should respect the underlying physics of the calculations they are supposed to model. Disregarding some of the physical constraints of the simulations, for instance that the forces acting on atoms should be the derivative of the energy, can make models faster to evaluate and train, as demonstrated in some recent work.In this paper, we argue that this particular constraint, also called energy conservation, is essential to perform physically meaningful simulations and that it should not be disregarded. We make this point both theoretically and through a series of experiments, which highlight different, sometimes subtle, ways in which simulations with such models can fail. We also discuss strategies to keep the speedup of disregarding energy conservation while avoiding unphysical simulation outcomes.