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Optimal Experimental Design for Inverse Problems in the Presence of Observation Correlations

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/21M1418666· OSTI ID:1910038
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Optimal experimental design (OED) is the general formalism of sensor placement and decisions on the data collection strategy for engineered or natural experiments. This problem is prevalent in many critical fields such as battery design, numerical weather prediction, geosciences, environmental and urban studies. State-of-the-art computational methods for experimental design do not accommodate correlation structure in observational errors produced by many expensive-to-operate devices such as X-ray machines, radars, and satellites. Discarding evident data correlations leads to biased results, higher expenses, and waste of valuable resources. We present a general formulation of the OED formalism for model-constrained large-scale Bayesian linear inverse problems, where measurement errors are generally correlated. The proposed approach utilizes the Hadamard product of matrices to formulate the weighted-likelihood, and is valid for both finite as well as infinite-dimensional Bayesian inverse problems. Extensive numerical experiments are carried out for empirical verification of the proposed approach using an advection-diffusion model, where the objective is to optimally place a small set of sensors, under a limited budget, to predict the concentration of a contaminant in a closed and bounded domain.
Research Organization:
Argonne National Laboratory (ANL)
Sponsoring Organization:
USDOE Office of Science - Office of Advanced Scientific Computing Research (ASCR); USDOE Office of Science
DOE Contract Number:
AC02-06CH11357
OSTI ID:
1910038
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Vol. 44; ISSN 1064-8275
Country of Publication:
United States
Language:
English

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Related Subjects

Correlated observations
Data assimilation
Inverse problems
Optimal Experimental Design