Respecting the boundaries: Space-filling designs for surrogate modeling with boundary information

Abstract

Gaussian process (GP) surrogate models are widely used for emulating expensive computer simulators, and have led to important advances in science and engineering. One challenge with fitting such surrogates is the costly generation of training data, which can require thousands of CPU hours per run. Recent promising work has investigated the integration of known boundary information within GP surrogates, which can greatly reduce its required training sample size and thus its computational cost. There is, however, little work exploring the critical question of how such simulation experiments should be designed given boundary information. We thus propose here a new class of space-filling designs, called boundary maximin designs, for effective GP surrogate modeling with boundary information. Our designs rely on a new space-filling criterion that is derived from the asymptotic D-optimal designs of the boundary GPs from Vernon et al. (2019) and Ding et al. (2019), which can incorporate a broad class of known boundaries, including axis-parallel and/or perpendicular boundaries. To account for effect sparsity with many variables, we further propose a new boundary maximum projection design that jointly integrates boundary information and ensures good projective properties. Numerical experiments and an application to solving expensive partial differential equations show the improved surrogate performance of boundary-integrated GPs using the proposed boundary maximin designs compared to the state-of-the-art.

Advisor(s)

Simon Mak

Bio

Yen-Chun is a 3rd year PhD student interested in experimental designs and sequential decision making.