From point estimates to feasible regions: Probabilistic and physics-informed inversion of thermoreflectance measurements

Thermoreflectance techniques are widely used to extract interfacial thermal conductance (ITC) and thermal conductivity from time-domain thermoreflectance (TDTR) signals. However, when multiple parameters are coupled, the extent to which their physical values can be uniquely recovered from experimental data remains unclear. In this work, we investigate this issue for an Al/GaN system using Bayesian and machine-learning approaches. Sensitivity analysis and root-mean-square error (RMSE) landscape mapping show that ITC and substrate thermal conductivity ksub affect the TDTR response differently but are not fully separable. Consequently, multiple correlated parameter combinations can produce similar thermal responses. Joint Bayesian parameter estimation (BPE) further quantifies this behavior by revealing a finite, strongly correlated posterior region in the ITC-–ksub parameter space rather than an isolated solution. To enable rapid probabilistic inference, we further develop a physics-informed multivariate Gaussian regression network (PMGRN) that directly predicts the means, standard deviations, and correlation coefficient of ITC and ksub. A physics-based loss coupled to the TDTR forward solver constrains the predicted parameter combinations to remain consistent with the measured thermal response. After training, PMGRN reduces the inference time from hours for the present full-grid BPE implementation to approximately 1 s for a new in-domain measurement. These results show that, although the underlying thermal properties have definite physical values, the experimentally accessible inverse result can remain distributed over a correlated, probability-weighted region because of parameter coupling and limited identifiability. Thermoreflectance inversion should, therefore, report not only a representative parameter estimate but also the uncertainty and correlation structure supported by the measurement.