Uncertainty Analysis for Drift-Diffusion Equations

TL;DR

This paper investigates how randomness in parameters affects drift-diffusion equations, especially in pedestrian dynamics, by analyzing quantities of interest with probabilistic stability, extending deterministic results to uncertain data.

Contribution

It introduces a probabilistic framework for analyzing drift-diffusion equations with uncertain parameters, focusing on quantities of interest rather than sensitivity analysis.

Findings

Existence and stability established for deterministic problem.

Probabilistic continuity results for quantities of interest.

Framework applicable to non-conservative mass scenarios.

Abstract

We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After providing existence and stability for the deterministic problem, we consider uncertainty in the data. Instead of a sensitivity analysis we propose to measure functionals of the solution, so-called quantities of interest (QoI), by involving scalarizing statistics. For these summarizing statistics we provide probabilistic continuity results.