Data-driven computation methods for quasi-stationary distribution and sensitivity analysis

TL;DR

This paper introduces a data-driven computational approach for quasi-stationary distributions (QSDs) using Fokker-Planck equations and coupling methods to analyze sensitivity, supported by numerical experiments.

Contribution

It proposes a novel data-driven solver for QSDs based on optimization of Fokker-Planck equations and applies coupling techniques for sensitivity analysis.

Findings

The solver effectively computes QSDs from data.

Sensitivity of QSDs to boundary and diffusion changes can be quantitatively estimated.

Numerical results demonstrate the method's accuracy and applicability.

Abstract

This paper studies computational methods for quasi-stationary distributions (QSDs). We first proposed a data-driven solver that solves Fokker-Planck equations for QSDs. Similar as the case of Fokker-Planck equations for invariant probability measures, we set up an optimization problem that minimizes the distance from a low-accuracy reference solution, under the constraint of satisfying the linear relation given by the discretized Fokker-Planck operator. Then we use coupling method to study the sensitivity of a QSD against either the change of boundary condition or the diffusion coefficient. The 1-Wasserstein distance between a QSD and the corresponding invariant probability measure can be quantitatively estimated. Some numerical results about both computation of QSDs and their sensitivity analysis are provided.