Subspace accelerated measure transport methods for fast and scalable sequential experimental design, with application to photoacoustic imaging

TL;DR

This paper introduces a scalable, derivative-based method for sequential experimental design in high-dimensional Bayesian inverse problems, improving efficiency in computing information gain and reducing dimensionality.

Contribution

It develops a unified framework combining measure transport and likelihood-informed subspace projection for efficient, high-dimensional sequential experimental design.

Findings

The proposed bound effectively guides design placement in PDE-based inverse problems.

The method enables scalable inference in high- and infinite-dimensional settings.

Numerical experiments show improved design efficiency using the new approach.

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 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.