Robust A-Optimal Experimental Design for Sensor Placement in Bayesian Linear Inverse Problems

Journal Article · Wed May 28 00:00:00 EDT 2025 · SIAM/ASA Journal on Uncertainty Quantification

DOI:https://doi.org/10.1137/24M1667543· OSTI ID:2589771

Attia, Ahmed ^[1]; Leyffer, Sven ^[1]; Munson, Todd S. ^[1]

---

1. Argonne National Laboratory (ANL), Argonne, IL (United States)

Optimal design of experiments for Bayesian inverse problems has recently gained wide popularity and attracted much attention, especially in the computational science and Bayesian inversion communities. An optimal design maximizes a predefined utility function that is formulated in terms of the elements of an inverse problem, an example being optimal sensor placement for parameter identification. The state-of-the-art algorithmic approaches following this simple formulation generally overlook misspecification of the elements of the inverse problem, such as the prior or the measurement uncertainties. This work presents an efficient algorithmic approach for designing optimal experimental design schemes for Bayesian linear inverse problems such that the optimal design is robust to misspecification of elements of the inverse problem. Specifically, we consider a worst-case scenario approach for the uncertain or misspecified parameters, formulate robust objectives, and propose an algorithmic approach for optimizing such objectives. Furthermore, both relaxation and stochastic solution approaches are discussed with detailed analysis and insight into the interpretation of the problem and the proposed algorithmic approach. Extensive numerical experiments to validate and analyze the proposed approach are carried out for sensor placement in a parameter identification problem.

• Research Organization: Argonne National Laboratory (ANL), Argonne, IL (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
• Grant/Contract Number: AC02-06CH11357
• OSTI ID: 2589771
• Journal Information: SIAM/ASA Journal on Uncertainty Quantification, Journal Name: SIAM/ASA Journal on Uncertainty Quantification Journal Issue: 2 Vol. 13; ISSN 2166-2525
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• Country of Publication: United States
• Language: English

Related Subjects

Bayesian inverse problems
Bayesian inversion
Expected information gain
Optimal design of experiments
Robust experimental design
binary optimization
design of experiments
robust optimization
stochastic learning