Enhancing robustness in machine-learning-accelerated molecular dynamics: A multi-model nonparametric probabilistic approach

In this work, we present a system-agnostic probabilistic framework to quantify model-form uncertainties in molecular dynamics (MD) simulations based on machine-learned (ML) interatomic potentials. Such uncertainties arise from the design and selection of ML potentials, as well as from training aspects pertaining to the definition of datasets and calibration strategies. Our approach relies on a stochastic reduced-order model (SROM) where the approximation space is expanded through the randomization of the projection basis. The construction of the underlying probability measure is achieved in the context of information theory, by leveraging the existence of multiple model candidates, corresponding to different ML potentials for instance. To assess the effectiveness of the proposed approach, the method is applied to capture model-form uncertainties in a sodium thiophosphate system, relevant to sodium-ion-state batteries. We demonstrate that the SROM accurately encodes model uncertainties from different ML potentials - including a Neuro-Evolution Potential (NEP) and a Moment Tensor Potential (MTP) - and can be used to propagate these uncertainties to macroscopic quantities of interest, such as ionic diffusivity. Additionally, we investigate the impact of augmenting the snapshot matrix with momenta, and of introducing a frequency-based split in the construction of the random projection matrix. Results indicate that including momenta improves the accuracy of the SROM, while frequency splitting enables stabilization around nominal responses during uncertainty propagation. The proposed enhancements contribute to more robust and stable predictions in MD simulations involving ML potentials.