GTSM: Gaussian Splatting with Thermal State-Space Dynamics for Spatio-Temporal Thermal Field Reconstruction and Prediction

Yunpeng Zhao, Haoxiang Zhang, Chao Liu

Temperature-field reconstruction and prediction are important for condition monitoring, process analysis, and state assessment in industrial and dynamic environments. This work aims to recover a four-dimensional spatio-temporal thermal state field directly from two-dimensional observations, without requiring a predefined 3D model, prescribed thermodynamic equation, or predefined heating/cooling trajectory. To this end, we propose the Gaussian Thermal State-Space Model (GTSM), which represents thermal evolution through a shared scene-level latent process and Gaussian-specific local thermal states. The resulting continuous dynamics are propagated using differentiable RK2 integration, allowing thermal evolution to be inferred from multi-view and multi-temporal observations and continuously extrapolated beyond the observed interval. GTSM is designed as a backbone-agnostic thermal dynamics module for Gaussian representations and can be integrated with both static 3D Gaussian Splatting and dynamic 4D Gaussian Splatting, supporting thermal reconstruction and prediction under both static and time-varying target geometry. The reconstructed representation further enables novel-view thermal…