Subspace accelerated measure transport methods for fast and scalable sequential experimental design, with application to photoacoustic imaging
For practitioners of Bayesian inverse problems with expensive models, this work provides a computationally feasible approach to sequential experimental design in high-dimensional, non-Gaussian settings.
The paper introduces a scalable method for sequential optimal experimental design in Bayesian inverse problems, using a derivative-based upper bound to guide design placement and enable dimension reduction. Numerical experiments on PDE-governed inverse problems show effective designs.
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 expected information gain (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 partial differential equations (PDEs) demonstrate the effectiveness of designs by maximizing the proposed bound.