paper

Physics-Derived Natural Coordinates for Fast Uncertainty Propagation in Multilayer Thermoreflectance

arXiv:2610.09192 · doi:10.1016/j.ijheatmasstransfer.2026.129653

Abstract

Uncertainty quantification in thermoreflectance measurements of multilayer structures is challenging because thermophysical-property extraction involves nonlinear inverse problems with strongly coupled parameters. Covariance-based analytical propagation is efficient but assumes local linearity and approximately Gaussian fitted variables, whereas Monte Carlo (MC) propagation captures non-Gaussian behavior but is computationally expensive and can be unreliable when simultaneously fitting parameters spanning very different orders of magnitude. Here, we address these issues by combining normalized MC sampling, used to obtain reliable benchmark distributions, with physics-based variable transformations for analytical uncertainty propagation. From the multilayer heat-diffusion equation, we identify natural coordinates: the interfacial thermal resistance 1/G, the substrate combinations sqrt(k_z k_r) and sqrt(k_z C), and the thin-film combinations k_r/C, hC, and Ch^2/k_z. Across several representative multilayer systems and thermoreflectance modalities, these coordinates are approximately Gaussian even when the original physical parameters are skewed. Performing covariance-based propagation in the transformed space and mapping the results back to physical parameters yields asymmetric confidence intervals that closely match normalized MC benchmarks. The approach preserves the non-Gaussian uncertainty structure of the recovered parameters while avoiding repeated nonlinear refitting, providing a fast and physically interpretable methodology for thermoreflectance uncertainty quantification in multilayer systems governed by diffusive heat conduction.

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