2022/01/01 by Eric Simonnet · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Artificial intelligence #Computer science #Deep learning #Economics #Model Reduction and Neural Networks #Statistical Mechanics and Entropy
paper · doi:10.1016/j.jcp.2023.112349
published in Journal of Computational Physics 491, 112349 (Elsevier BV)
openalex publication_date 2022/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Predicting the occurrence of rare and extreme events in complex systems is a well-known problem in non-equilibrium physics. These events can have huge impacts on human societies. New approaches have emerged in the last ten years, which better estimate tail distributions. They often use large deviation concepts without the need to perform heavy direct ensemble simulations. In particular, a well-known approach is to derive a minimum action principle and to find its minimizers.The analysis of rare reactive events in non-equilibrium systems without detailed balance is notoriously difficult either theoretically and computationally. They are described in the limit of small noise by the Freidlin-Wentzell action. We propose here a new method which minimize the geometrical action instead using neural networks: it is called deep gMAM. It relies on a natural and simple machine-learning formulation of the classical gMAM approach. We give a detailed description of the method as well as many examples. These include bimodal switches in complex stochastic (partial) differential equations, quasi-potential estimates, but also extreme events in Burgers turbulence.