Computing non-equilibrium trajectories by a deep learning approach

TL;DR

This paper introduces deep gMAM, a neural network-based method for efficiently computing non-equilibrium trajectories and rare events in complex stochastic systems, improving the estimation of tail distributions without heavy simulations.

Contribution

It presents a novel deep learning approach to minimize geometrical action for rare event analysis, extending the classical gMAM method with neural networks.

Findings

Successfully applied to bimodal switches in stochastic PDEs

Accurately estimates quasi-potential landscapes

Effectively models extreme events in turbulence

Abstract

Predicting the occurence 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 minimizes 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, and extreme events in Burgers turbulence.