Uncertainty in AI-driven Monte Carlo simulations

Abstract

In the study of complex systems, evaluating physical observables often requires sampling representative configurations via Monte Carlo techniques. These methods rely on repeated evaluations of the system's energy and force fields, which can become computationally expensive. To accelerate these simulations, deep learning models are increasingly employed as surrogate functions to approximate the energy landscape or force fields. However, such models introduce epistemic uncertainty in their predictions, which may propagate through the sampling process and affect the simulation's macroscopic behavior. In our work, we present the Penalty Ensemble Method (PEM) to quantify epistemic uncertainty and mitigate its impact on Monte Carlo sampling. Our approach introduces an uncertainty-aware modification of the Metropolis acceptance rule, which increases the rejection probability in regions of high uncertainty, thereby enhancing the reliability of the simulation outcomes.

References in corpus (11)

• Machine learning and the physical sciences
• Machine learning for molecular simulation
• Towards Exact Molecular Dynamics Simulations with Machine-Learned Force Fields
• Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisons
• Performance Assessment of Universal Machine Learning Interatomic Potentials: Challenges and Directions for Materials' Surfaces
• Uncertainty estimation for molecular dynamics and sampling
• The Penalty Method for Random Walks with Uncertain Energies
• A Survey on Epistemic (Model) Uncertainty in Supervised Learning: Recent Advances and Applications
• Efficient Modelling of Trivializing Maps for Lattice ${\varphi }^4$ Theory Using Normalizing Flows: A First Look at Scalability
• Towards out of distribution generalization for problems in mechanics
• Performance of machine-learning-assisted Monte Carlo in sampling from simple statistical physics models