A Machine-Learning-Based Importance Sampling Method to Compute Rare Event Probabilities

TL;DR

This paper introduces a machine-learning-enhanced importance sampling method for efficiently estimating rare event probabilities in nonlinear dynamical systems, leveraging surrogate models to reduce computational costs.

Contribution

It presents a novel approach combining Bayesian inverse problems with machine learning surrogates to improve rare event probability estimation.

Findings

Surrogate models significantly reduce computational costs.

The method accurately estimates extreme excursion probabilities.

Applicable to high-dimensional nonlinear systems.

Abstract

We develop a novel computational method for evaluating the extreme excursion probabilities arising from random initialization of nonlinear dynamical systems. The method uses excursion probability theory to formulate a sequence of Bayesian inverse problems that, when solved, yields the biasing distribution. Solving multiple Bayesian inverse problems can be expensive; more so in higher dimensions. To alleviate the computational cost, we build machine-learning-based surrogates to solve the Bayesian inverse problems that give rise to the biasing distribution. This biasing distribution can then be used in an importance sampling procedure to estimate the extreme excursion probabilities.