GPU-Accelerated Particle Methods for Evaluation of Sparse Observations for PDE-Constrained Inverse Problems
For researchers solving inverse problems with sparse observations, this work offers computationally efficient methods that leverage modern GPU architectures.
The paper presents two GPU-accelerated particle methods for efficiently computing the forward map in PDE-constrained inverse problems, enabling substantial speedup for applications with sparse observations and high-dimensional unknowns.
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.