Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations
Numerical Analysis
2022-06-08 v1 Numerical Analysis
Abstract
We present a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria utilizing adjoint-based a posteriori error analysis for differential equations. This is in contrast to classical MLMC algorithms that use either a hierarchy of uniform meshes or adaptively refined meshes based on Richardson extrapolation, and employ a stopping criteria that relies on assumptions on the convergence rate of the MLMC levels. This work develops two adaptive refinement strategies for the MLMC algorithm. These strategies are based on a decomposition of an error estimate of the MLMC bias and utilize variational analysis, adjoint problems and computable residuals.
Cite
@article{arxiv.2206.02905,
title = {Adjoint-based Adaptive Multi-Level Monte Carlo for Differential Equations},
author = {Jehanzeb Chaudhry and Zachary Stevens},
journal= {arXiv preprint arXiv:2206.02905},
year = {2022}
}