Robust A-Optimal Experimental Design for Bayesian Inverse Problems
This work addresses robustness issues in optimal experimental design for computational science and Bayesian inversion communities, representing an incremental improvement over existing methods.
The paper tackles the problem of optimal experimental design for Bayesian inverse problems being sensitive to misspecifications in model elements like priors or measurement uncertainties, and presents an efficient algorithmic approach that formulates robust objectives using worst-case scenarios, validated through numerical experiments on sensor placement for parameter identification.
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 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. 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.