1. GPU-accelerated particle methods for evaluation of sparse observations for inverse problems constrained by diffusion PDEs.
- Author
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Borggaard, Jeff, Glatt-Holtz, Nathan, and Krometis, Justin
- Subjects
- *
INVERSE problems , *DIFFUSION , *DIRICHLET problem , *EVALUATION methodology , *MODERN architecture , *DIFFUSION coefficients - 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 Dirichlet boundary-value problems. 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. • Particle algorithms are presented for PDE-constrained inverse problems. • The methods leverage problem structure to enable fast computation of the forward map. • The methods scale in a natural fashion to modern computational architectures. • Computational complexity for these and traditional two-step algorithms is provided. • Applications to Bayesian inference and numerical optimization are provided. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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