Computational Inverse Problems Governed by PDEs

Centering on computational strategies for inverse problems governed by partial differential equations, the text unifies deterministic inversion techniques with Bayesian methods. It delves into post?optimality sensitivity analysis, optimal experiment design, and inversion under model uncertainty, backed by theory, examples, and exercises. This textbook focuses on computational methods for inverse problems that are governed by partial differential equations (PDEs). The author considers deterministic and Bayesian formulations and highlights how traditional tools from deterministic inversion can be integrated into solution methods for Bayesian inverse problems. Advanced topics such as post-optimality sensitivity analysis, optimal design of experiments, and Bayesian inversion under model uncertainty are also included. Computational Inverse Problems Governed by PDEs offers readers a balance of theoretical and computational insight, an example-driven approach that provides an accessible presentation, and over 150 theoretical and computational exercises.