# Graduate Student / Postdoc Seminar

#### Multifidelity Monte Carlo methods for uncertainty quantification

**Speaker:**
Ben Peherstorfer, Courant Institute of Mathematical Sciences

**Location:**
Warren Weaver Hall 1302

**Date:**
Friday, February 15, 2019, 1 p.m.

**Synopsis:**

Monte Carlo methods in uncertainty quantification typically form a loop around a computational model and evaluate the model in each iteration at new realizations of inputs, parameter configurations, and coefficients. Using a high-fidelity model in each iteration guarantees high accuracy but often quickly exceeds available computational resources because of the high costs of solving high-fidelity models. Replacing the high-fidelity model with a low-cost, low-fidelity model (surrogate) can lead to significant speedups but introduces an approximation error that is often hard to quantify and control. This talk surveys multifidelity methods that combine, instead of replace, the high-fidelity model with low-fidelity models. The overall premise of multifidelity Monte Carlo methods is that low-fidelity models are leveraged for variance reduction while occasional recourse is made to the high-fidelity model to establish unbiasedness. The focus of the presentation is on optimally adapting low-fidelity models and on constructing transport-map-based preconditioners for Markov chain Monte Carlo. Numerical results demonstrate that multifidelity methods can achieve significant speedups compared to methods that rely on a single model alone.