GPU-accelerated particle methods for evaluation of sparse observations for inverse problems constrained by diffusion PDEs

JOURNAL OF COMPUTATIONAL PHYSICS

卷:391

Article

Borggaard, Jeff¹  Glatt-Holtz, Nathan²  Krometis, Justin³ 

[1] Virginia Tech, Dept Math, Blacksburg, VA 24061 USA

[2] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[3] Virginia Tech, Adv Res Comp, Blacksburg, VA 24061 USA

关键词: Inverse problems;    Optimization;    Scientific computing;    Parallel computing;    Passive scalars;   

DOI  :  10.1016/j.jcp.2019.04.034

来源: Elsevier

【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free