A BAYESIAN SPATIO-TEMPORAL MODELING APPROACH TO THE INVERSE HEAT CONDUCTION PROBLEM

A wide range of science and engineering problems involve inferring the system behavior and the physical models from indirect observations. These are known as inverse problems. Unlike forward problems (predictive models), inverse problems are difficult to solve due to ill-posedness arising from one or more of non-existence, non-uniqueness (existence of many solutions), or instability (small perturbations in the measurements emerging from noise could lead to large changes in the solution). Therefore, direct inversion of the inverse problem in complex real-world systems is impractical. Several modeling approaches have been developed and adopted in the literature. However, the existing approaches do not consider spatio-temporal relationships. Meanwhile, various real systems and processes exist whose inverse problems can be comfortably modeled using spatio-temporal modeling techniques. We present a spatio-temporal inverse model considering interaction effects for modeling this type of inverse problem. We adopted a Bayesian inference framework for the subsequent parameter estimation problem and developed a Gibbs sampling algorithm to sample from the posterior distribution of the parameter of interest. Finally, we evaluate the proposed modeling technique and solution framework using several case studies of inverse problems in diverse heat conduction domains. Compared with conventional methods, the proposed framework performs better and can be adopted for solving inverse problems with spatio-temporal properties in various scientific and engineering domains.