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Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network

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Abstract

We address the solution of large-scale Bayesian optimal experimental design (OED) problems governed by partial differential equations (PDEs) with infinite-dimensional parameter fields. The OED problem seeks to find sensor locations that maximize the expected information gain (EIG) in the solution of the underlying Bayesian inverse problem. Computation of the EIG is usually prohibitive for PDE-based OED problems. To make the evaluation of the EIG tractable, we approximate the (PDE-based) parameter-to-observable map with a derivative-informed projected neural network (DIPNet) surrogate, which exploits the geometry, smoothness, and intrinsic low-dimensionality of the map using a small and dimension-independent number of PDE solves. The surrogate is then deployed within a greedy algorithm-based solution of the OED problem such that no further PDE solves are required. We analyze the EIG approximation error in terms of the generalization error of the DIPNet and show they are of the same order. Finally, the efficiency and accuracy of the method are demonstrated via numerical experiments on OED problems governed by inverse scattering and inverse reactive transport with up to 16,641 uncertain parameters and 100 experimental design variables, where we observe up to three orders of magnitude speedup relative to a reference double loop Monte Carlo method.

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Funding

This research was partially funded by DOE ASCR DE-SC0019303 and DE-SC0021239, DOD MURI FA9550-21-1-0084, and NSF DMS-2012453.

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Authors and Affiliations

  1. Department of Mathematics, The University of Texas at Austin, 2515 Speedway, Austin, TX, 78712, USA

    Keyi Wu

  2. Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 E 24th St, Austin, TX, 78712, USA

    Thomas O’Leary-Roseberry & Omar Ghattas

  3. School of Computational Science and Engineering, Georgia Institute of Technology, Atlanta, GA, 30308, USA

    Peng Chen

  4. Departments of Geological Sciences and Mechanical Engineering, The University of Texas at Austin, Austin, 78712, TX, USA

    Omar Ghattas

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  1. Keyi Wu
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Wu, K., O’Leary-Roseberry, T., Chen, P. et al. Large-Scale Bayesian Optimal Experimental Design with Derivative-Informed Projected Neural Network. J Sci Comput 95, 30 (2023). https://doi.org/10.1007/s10915-023-02145-1

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