Scalable Method for Bayesian Experimental Design without Integrating over Posterior Distribution

SIAM/ASA Journal on Uncertainty Quantification, vol. 13, pp. 114–139

Abstract

Abstract. We address the computational efficiency of finding the A-optimal Bayesian experimental design, where the observation map is based on partial differential equations and thus computationally expensive to evaluate. A-optimality is a widely used and easily interpreted criterion, that seeks the optimal experimental design by minimizing the expected conditional variance. Our study presents a novel likelihood-free approach to the A-optimal experimental design that does not require sampling or integration over the Bayesian posterior distribution. In our proposed approach, we estimate the expected conditional variance via the variance of the conditional expectation and approximate the conditional expectation using its orthogonal projection property. We derive an asymptotic error estimate for the proposed estimator of the expected conditional variance and verify it with numerical experiments. Furthermore, we extend our approach to the case where the domain of the experimental design parameters is continuous. Specifically, we propose a nonlocal approximation of the conditional expectation using an artificial neural network and apply transfer learning and data augmentation to reduce the number of evaluations of the measurement model. Through numerical experiments, we demonstrate that our method greatly reduces the number of measurement model evaluations compared with widely used importance sampling-based approaches. Code is available at https://github.com/vinh-tr-hoang/DOEviaPACE .

Authors 4

1. Truong‐Vinh Hoang Aachen Department of Mathematics Chair of Mathematics for Uncertainty Quantification

   RWTH Aachen University

   Affiliation as printed

   Chair of Mathematics for Uncertainty Quantification, Department of Mathematics, RWTH-Aachen University, 52056 Aachen, Germany

2. Luis Espath

   University of Nottingham

   Affiliation as printed

   Faculty of Science, University of Nottingham, Nottingham, England

3. Sebastian Krumscheid

   Karlsruhe Institute of Technology

   Affiliation as printed

   Scientific Computing Center and Institute for Applied and Numerical Mathematics, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany

4. Raul F. Tempone Aachen Computer

   RWTH Aachen University · King Abdullah University of Science and Technology

   Affiliation as printed

   Computer, Electrical and Mathematical Sciences and Engineering, KAUST, Saudi Arabia, and Alexander von Humboldt professor in Mathematics of Uncertainty Quantification, RWTH Aachen University, Germany