Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network

We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that maximize expected information gain (EIG) in underlying inverse problem. Computation EIG is usually prohibitive for PDE-based problems. To make evaluation tractable, we approximate (PDE-based) parameter-to-observable map a derivative-informed projected neural network (DIPNet) surrogate, which exploits geometry, smoothness, and intrinsic low-dimensionality using small dimension-independent number PDE solves. surrogate then deployed within greedy algorithm-based such no further solves are required. analyze approximation error terms generalization DIPNet show they same order. Finally, efficiency accuracy method demonstrated via numerical experiments on scattering reactive transport up 16,641 uncertain parameters 100 variables, where observe three orders magnitude speedup relative reference double loop Monte Carlo method.