  We consider optimal experimental design (OED) problems in selecting the most
informative observation sensors to estimate model parameters in a Bayesian
framework. Such problems are computationally prohibitive when the
parameter-to-observable (PtO) map is expensive to evaluate, the parameters are
high-dimensional, and the optimization for sensor selection is combinatorial
and high-dimensional. To address these challenges, we develop an accurate,
scalable, and efficient computational framework based on derivative-informed
neural operators (DINOs). The derivative of the PtO map is essential for
accurate evaluation of the optimality criteria of OED in our consideration. We
take the key advantage of DINOs, a class of neural operators trained with
derivative information, to achieve high approximate accuracy of not only the
PtO map but also, more importantly, its derivative. Moreover, we develop
scalable and efficient computation of the optimality criteria based on DINOs
and propose a modified swapping greedy algorithm for its optimization. We
demonstrate that the proposed method is scalable to preserve the accuracy for
increasing parameter dimensions and achieves high computational efficiency,
with an over 1000x speedup accounting for both offline construction and online
evaluation costs, compared to high-fidelity Bayesian OED solutions for a
three-dimensional nonlinear convection-diffusion-reaction example with tens of
thousands of parameters.
