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

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Simulation-based optimal Bayesian experimental design for nonlinear systems (2011, methodology): “The method is similar to a steepest-descent method using finite difference estimates of the gradient, except that SPSA only uses two random perturbations to estimate the gradient regardless of the problem’s dimension: dk+1 = dk − akgk(dk) (11) gk(dk) = Û(dk + ck∆k)− Û(dk − ck∆k) 2ck”
Bayesian inference with optimal maps (2011, background): “Keywords: Bayesian inference, optimal transport, measure-preserving maps, inverse problems, polynomial chaos, numerical optimization”
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “The paper [100] compares projection-based reduced models to stochastic spectral approximations in a statistical inverse problem setting and concludes that, for an elliptic problem with low parameter dimension, the reduced model requires fewer oﬄine simulations to achieve a desired level of…”
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems (2020, background): “Often, the solution of an inverse problem can be computationally expensive due to the potentially millions of forward model evaluations needed for estimator evaluation or characterization of posterior distributions of physical parameters [96].”