Exploring and Optimizing Computational Models with Gaussian Processes

As science advances, increasingly sophisticated and intensive computational models are required to explain new phenomena, and these models lie increasingly beyond our intuition. It is therefore important to develop tools to efficiently conduct sensitivity analyses and calibration of such models. In this talk, we will begin by developing a closed form expression for a Gaussian process estimator of a popular type of linear sensitivity analysis based on gradients, the Active Subspace method. Subsequently, we will develop sequential design procedures which allow for estimation of this sensitivity analysis in expensive to evaluate settings. Next, we study the behavior of surrogate-estimated active subspaces on models which exhibit jump-discontinuities, such as agent-based models and transonic fluid models. Though such models are not continuous, nevermind differentiable, we find that the analysis still yields a meaningful analysis. Finally, we introduce some heuristics for conducting large-scale, high dimensional Bayesian optimization without gradient information.