Multifidelity Uncertainty Quantification for Nonlocal Models

Parisa Khodabakhshi (U of Texas, Austin)

May 04. 2022, 15:45 — 16:15

Nonlocal models are useful at describing certain physical phenomena for which conventional PDEs fail to describe the behavior. In nonlocal models, distant interactions are considered between points that are less than a finite length scale (usually referred to as the horizon) apart from each other. As a result of distant interactions, nonlocal models are generally computationally more expensive than their local counterparts due to the reduced sparsity. The higher computational cost of nonlocal models might inhibit the implementation of an outer-loop application (e.g., uncertainty quantification, optimization, inference, control) where multiple model evaluations are required. Employing a multifidelity method for nonlocal models that combines surrogate models of lower fidelity with the high-fidelity model can help eliminate this constraint. We propose a multifidelity approach for a nonlocal diffusion model to be used in an uncertainty quantification setting. The surrogate models are built by reducing the mesh refinement, the horizon, or both. The multifidelity method achieves the speed-up in Monte Carlo estimations of the quantity of interest by allocating most model evaluations to the cheap surrogate models while keeping high-fidelity model evaluations at a relatively low number. It is shown that the multifidelity method achieves above two order of magnitude speed-ups compared to the high-fidelity model.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zurich)
Sara van de Geer (ETH Zurich)
Karen Willcox (U of Texas, Austin)