GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for PDE-Constrained Inverse Problems

Jeff Borggaard; Nathan E. Glatt-Holtz; Justin A. Krometis

doi:10.1016/j.jcp.2019.04.034

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arXiv · 1808.10580

GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for PDE-Constrained Inverse Problems

Jeff Borggaard·Nathan E. Glatt-Holtz·Justin A. Krometis

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Abstract

We consider the inverse problem of estimating parameters of a driven diffusion (e.g., the underlying fluid flow, diffusion coefficient, or source terms) from point measurements of a passive scalar (e.g., the concentration of a pollutant). We present two particle methods that leverage the structure of the inverse problem to enable efficient computation of the forward map, one for time evolution problems and one for a Dirichlet boundary-value problem. The methods scale in a natural fashion to modern computational architectures, enabling substantial speedup for applications involving sparse observations and high-dimensional unknowns. Numerical examples of applications to Bayesian inference and numerical optimization are provided.

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Jeff Borggaard, Nathan E. Glatt-Holtz, Justin A. Krometis. 2018-08-31. GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for PDE-Constrained Inverse Problems. https://doi.org/10.1016/j.jcp.2019.04.034

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