Bayesian inverse problems for partial differential equations with discontinuous coefficients: an adaptive finite element approach - Oh, Wei Yuan (Nanyang Technological University, 2025)
This thesis addresses a challenging class of inverse problems in which one seeks to identify an inclusion within a physical domain by observing noisy, indirect measurements of the underlying system. We adopt a Bayesian framework, treating the unknown parameters as random variables and combining prior information with observational data to form a posterior distribution. This approach naturally quantifies the uncertainty in the inferred inclusion and enables rigorous statistical interpretation of the results.