Subspace Accelerated Measure Transport Methods for Fast and Scalable Sequential Experimental Design, with Application to Photoacoustic Imaging

Abstract. We propose a novel approach for sequential optimal experimental design (sOED) for Bayesian inverse problems involving expensive models with high-dimensional unknown parameters. This work focuses on designs that maximize the expected information gain (EIG) from prior to posterior, a task that is computationally very challenging in non-Gaussian settings. This challenge is amplified in sOED, as the incremental EIG (iEIG) must be repeatedly approximated across distinct stages, with both prior and posterior distributions being intractable. To address this, we derive a general-purpose, derivative-based upper bound for the iEIG, which not only guides design placement but also enables the construction of projectors onto likelihood-informed subspaces, facilitating parameter dimension reduction. By combining this approach with conditional measure transport maps for the sequence of posteriors, we develop a unified sOED and amortized inference framework scalable to high- and infinite-dimensional problems. Numerical experiments for two inverse problems governed by PDEs demonstrate the effectiveness of designs by maximizing the proposed bound.