Search

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]