Uncertainty in AI-driven Monte Carlo simulations

Condensed Matter > Disordered Systems and Neural Networks [Submitted on 17 Jun 2025 (v1), last revised 16 Jun 2026 (this version, v3)] Title:Uncertainty in AI-driven Monte Carlo simulations View PDF HTML (experimental)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. Submission history From: Dimitrios Tzivrailis [view email][v1] Tue, 17 Jun 2025 14:58:39 UTC (407 KB) [v2] Tue, 1 Jul 2025 14:09:54 UTC (326 KB) [v3] Tue, 16 Jun 2026 13:15:40 UTC (303 KB) Current browse context: cond-mat.dis-nn Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.