Designing a set of criteria for evaluating artificial neural networks trained with physics-based data to replicate molecular dynamics and other particle method trajectories

This article presents an in-depth analysis and evaluation of artificial neural networks (ANNs) when applied to replicate trajectories in molecular dynamics (MD) simulations or other particle methods. This study focuses on several architectures—feedforward neural networks (FNNs), convolutional neural networks (CNNs), recurrent neural networks (RNNs), time convolutions (TCs), self-attention (SA), graph neural networks (GNNs), neural ordinary differential equation (ODENets), and an example of physics-informed machine learning (PIML) model—assessing their effectiveness and limitations in understanding and replicating the underlying physics of particle systems. Through this analysis, this paper introduces a comprehensive set of criteria designed to evaluate the capability of ANNs in this context. These criteria include the minimization of losses, the permutability of particle indices, the ability to predict trajectories recursively, the conservation of particles, the model’s handling of boundary conditions, and its scalability. Each network type is systematically examined to determine its strengths and weaknesses in adhering to these criteria. While, predictably, none of the networks fully meets all criteria, this study extends beyond the simple conclusion that only by integrating physics-based models into ANNs is it possible to fully replicate complex particle trajectories. Instead, it probes and delineates the extent to which various neural networks can “understand” and interpret aspects of the underlying physics, with each criterion targeting a distinct aspect of this understanding.