Sparse polynomial chaos expansions for uncertainty quantification in thermal tomography

• Published in: Journal of computational and applied mathematics 2024-01, Vol.436, p.115406, Article 115406
• Main Authors: Sýkora, Jan, Havelka, Jan
• Format: Article
• Language: English
• Subjects: Bayesian inference; Sparse polynomial chaos; Thermal tomography
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2023.115406

This contribution presents the identification strategy of thermal parameters relying solely on data measured on boundaries — thermal tomography. The idea is to obtain crucial information about the thermal properties inside the domain under consideration while keeping the test sample intact. Such methodology perfectly fits into historic preservation where it is of particular interest to perform only non-destructive surface measurements. We propose an advanced, accelerated, and reliable inverse solver for thermal tomography problems. Here, Bayesian inference is addressed as a method, where unknown parameters are modeled as random variables regularizing the inverse problem. The obtained results are probability distributions – posterior distributions – summarizing all available information and any remaining uncertainty in the values of thermal parameters. Novelties of our approach consist in the combination of (i) formulation of parameter identification in a probabilistic setting, and (ii) use of the surrogate models based on the sparse polynomial chaos expansion. This new sparse formulation significantly reduces the total number of polynomial terms and represents the main achievement of this paper.