Uncertainty quantification in complex systems using approximate solvers

TL;DR

This paper introduces a new uncertainty quantification framework that efficiently combines approximate models with advanced Monte Carlo and Bayesian methods to accurately assess uncertainties in complex systems with reduced computational costs.

Contribution

It presents a rigorous approach to using inexpensive, approximate models within uncertainty quantification, enabling accurate statistical analysis with lower computational effort.

Findings

Accurate uncertainty estimates are achievable even with poor approximate models.

The framework provides rigorous confidence bounds at all stages.

Significant computational savings are demonstrated in complex system analyses.

Abstract

This paper proposes a novel uncertainty quantification framework for computationally demanding systems characterized by a large vector of non-Gaussian uncertainties. It combines state-of-the-art techniques in advanced Monte Carlo sampling with Bayesian formulations. The key departure from existing works is the use of inexpensive, approximate computational models in a rigorous manner. Such models can readily be derived by coarsening the discretization size in the solution of the governing PDEs, increasing the time step when integration of ODEs is performed, using fewer iterations if a non-linear solver is employed or making use of lower order models. It is shown that even in cases where the inexact models provide very poor approximations of the exact response, statistics of the latter can be quantified accurately with significant reductions in the computational effort. Multiple approximate models can be used and rigorous confidence bounds of the estimates produced are provided at all stages.