Work

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

Year: 2026

Type: article

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.

Source: SIAM/ASA Journal on Uncertainty Quantification

DOI: 10.1137/25m1735329

Authors: Tiangang Cui, Karina Koval, Roland Herzog, Robert Scheichl

Institutions: The University of Sydney, Heidelberg University

Language: English

Topic: Optimal Experimental Design Methods

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: green

Funders: Carl-Zeiss-Stiftung, Australian Research Council

Award: Dimension-robust and dynamical uncertainty quantification for digital twins