Optimal experimental design for prediction based on push-forward probability measures

Journal Article · Thu May 14 00:00:00 EDT 2020 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2020.109518· OSTI ID:1630281

Butler, T. ^[1]; Jakeman, J. D.  ^[2]; Wildey, T. ^[2]

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1. Univ. of Colorado, Denver, CO (United States)
2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Incorporating experimental data is essential for increasing the credibility of simulation-aided decision making and design. This paper presents a method which uses a computational model to guide the optimal acquisition of experimental data to produce data-informed predictions of quantities of interest (QoI). Many strategies for optimal experimental design (OED) select data that maximize some utility that measures the reduction in uncertainty of uncertain model parameters, for example the expected information gain between prior and posterior distributions of these parameters. In this paper, we seek to maximize the expected information gained from the pushforward of an initial (prior) density to the push-forward of the updated (posterior) density through the parameter-to-prediction map. The formulation presented is based upon the solution of a specific class of stochastic inverse problems which seeks a probability density that is consistent with the model and the data in the sense that the push-forward of this density through the parameter-to-observable map matches a target density on the observable data. While this stochastic inverse problem forms the mathematical basis for our approach, we develop a one-step algorithm, focused on push-forward probability measures, that leverages inference-for-prediction to bypass constructing the solution to the stochastic inverse problem. A number of numerical results are presented to demonstrate the utility of this optimal experimental design for prediction and facilitate comparison of our approach with traditional OED.

• Research Organization: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC04-94AL85000
• OSTI ID: 1630281
• Alternate ID(s): OSTI ID: 1630473
• Report Number(s): SAND2020-4951J; 686011; TRN: US2200651
• Journal Information: Journal of Computational Physics, Vol. 416, Issue C; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS