Toward Interpretable Multimodal Fusion: Heat Conduction Modeling for Hyperspectral and LiDAR Joint Classification

The fusion of hyperspectral (HS) and Light Detection and Ranging (LiDAR) data plays a crucial role in enhancing land-cover classification by jointly exploiting spectral, spatial, and structural cues. However, existing multimodal fusion methods still struggle to model long-range dependencies and complex anisotropic interactions while maintaining computational efficiency. This paper introduces M2Heat, a physics-inspired framework that investigates multimodal fusion through the lens of heat conduction. At its core, a physics-driven visual heat conduction module (vHeat) and enhanced Frequency Value Embeddings (FVEs) simulate anisotropic information flow, enabling the capture of global dependencies with sub-quadratic complexity and physical interpretability. This mechanism, combined with a hybrid spatial-frequency fusion strategy named Cross-Frequency Fusion (CFF) module, produces highly discriminative and robust feature representations. M2Heat achieves competitive overall performance on three benchmarks, i.e., Trento, Houston2013, and Augsburg, while providing an interpretable heat-conduction-guided perspective for multimodal feature fusion. These results indicate the potential of heat-conduction-guided neural operators for efficient and interpretable RS multimodal fusion. The source code is publicly available at https: /github.com/Weikan0425/M2Heat_HSI_LiDAR.