Surrogate and reduced-order modeling: a comparison of approaches for large-scale statistical inverse problems [Chapter 7]

Abstract

Solution of statistical inverse problems via the frequentist or Bayesian approaches described in earlier chapters can be a computationally intensive endeavor, particularly when faced with large-scale forward models characteristic of many engineering and science applications. High computational cost arises in several ways. First, thousands or millions of forward simulations may be required to evaluate estimators of interest or to characterize a posterior distribution. In the large-scale setting, performing so many forward simulations is often computationally intractable. Second, sampling may be complicated by the large dimensionality of the input space--as when the inputs are fields represented with spatial discretizations of high dimension--and by nonlinear forward dynamics that lead to multimodal, skewed, and/or strongly correlated posteriors. In this chapter, we present an overview of surrogate and reduced order modeling methods that address these computational challenges. For illustration, we consider a Bayesian formulation of the inverse problem. Though some of the methods we review exploit prior information, they largely focus on simplifying or accelerating evaluations of a stochastic model for the data, and thus are also applicable in a frequentist context.