Physics-Informed KAN-Mamba Model for Thermal Conductivity Estimation

Accurate thermal conductivity estimation remains difficult when engineering materials exhibit coupled temperature dependence, porosity, anisotropic fillers, and manufacturing-induced variability. This study proposes a physics-informed KAN-Mamba model that combines Kolmogorov-Arnold network transformations with a selective state-space backbone to estimate effective thermal conductivity from composition, microstructure, and boundary-condition descriptors. The method introduces a differentiable Fourier-consistency penalty, monotonic temperature regularization, and channel-wise spline activation to improve both numerical accuracy and physical plausibility. A benchmark containing 4,860 synthetic- measured samples across polymer composites, porous ceramics, aluminum alloys, and phase-change interface materials was constructed with five descriptor groups and three operating-temperature regimes. Compared with multilayer perceptron, random forest, temporal convolution, transformer, and pure Mamba baselines, the proposed model achieved an MAE of 0.137 W m−1 K−1, an RMSE of 0.214 W m−1 K−1, and an R2 of 0.982 on the held-out test set. The mean physics residual decreased by 47.6% relative to the unconstrained Mamba model, and the extrapolation error at 420-480 K was reduced from 0.412 to 0.246 W m−1 K−1. Ablation experiments show that removing the KAN transformation increased RMSE by 18.7%, while removing the physics-informed loss increased boundary-flux inconsistency by 52.3%. The results indicate that physically guided selective sequence modeling can provide a compact and reliable estimator for thermal design workflows involving sparse measurements and heterogeneous material families.