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Determination of the thermal properties of a material is an important task inmany scientific and engineering applications. How a material behaves whensubjected to high or fluctuating temperatures can be critical to the safety andlongevity of a system's essential components. The laser flash experiment is awell-established technique for indirectly measuring the thermal diffusivity,and hence the thermal conductivity, of a material. In previous works,optimization schemes have been used to find estimates of the thermalconductivity and other quantities of interest which best fit a given model toexperimental data. Adopting a Bayesian approach allows for prior beliefs aboutuncertain model inputs to be conditioned on experimental data to determine aposterior distribution, but probing this distribution using sampling techniquessuch as Markov chain Monte Carlo methods can be incredibly computationallyintensive. This difficulty is especially true for forward models consisting oftime-dependent partial differential equations. We pose the problem ofdetermining the thermal conductivity of a material via the laser flashexperiment as a Bayesian inverse problem in which the laser intensity is alsotreated as uncertain. We introduce a parametric surrogate model that takes theform of a stochastic Galerkin finite element approximation, also known as ageneralized polynomial chaos expansion, and show how it can be used to sampleefficiently from the approximate posterior distribution. This approach givesaccess not only to the sought-after estimate of the thermal conductivity butalso important information about its relationship to the laser intensity, andinformation for uncertainty quantification. We also investigate the effects ofthe spatial profile of the laser on the estimated posterior distribution forthe thermal conductivity.

Surrogate Accelerated Bayesian Inversion for the Determination of the Thermal Diffusivity of a Material