Graph-based prior and forward models for inverse problems on manifolds with boundaries
Abstract
This paper develops manifold learning techniques for the numerical solution of PDE-constrained Bayesian inverse problems on manifolds with boundaries. We introduce graphical Matérn-type Gaussian field priors that enable flexible modeling near the boundaries, representing boundary values by superposition of harmonic functions with appropriate Dirichlet boundary conditions. We also investigate the graph-based approximation of forward models from PDE parameters to observed quantities. In the construction of graph-based prior and forward models, we leverage the ghost point diffusion map algorithm to approximate second-order elliptic operators with classical boundary conditions. Numerical results validate our graph-based approach and demonstrate the need to design prior covariance models that account for boundary conditions.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jan 31, 2022
- Source ID
- 10.1088/1361-6420/ac3994
Entities
People
- Daniel Sanz-Alonso
- Hwanwoo Kim
- John Harlim
- Shixiao W Jiang
Organizations
- National Geospatial-Intelligence Agency
- National Science Foundation