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

arXiv: https://arxiv.org/abs/2610.26918 · HTML: https://mlsanity.com/paper/2610.26918/

## Key facts

- No citing papers in the map yet (data through 19 Oct 2026).
- Placed in 3D Gaussian splatting methods, one of 15 directions in 3D reconstruction and neural rendering.
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 17 Oct 2026.

## Placed in

- 3D reconstruction and neural rendering / [3D Gaussian splatting methods](https://mlsanity.com/recon3d/3d-gaussian-splatting-methods/)

## Builds on (most cited first, 17 of 17)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [4D Gaussian Splatting for Real-Time Dynamic Scene Rendering](https://mlsanity.com/paper/2310.08528/) (2023)
- [Deformable 3D Gaussians for High-Fidelity Monocular Dynamic Scene Reconstruction](https://mlsanity.com/paper/2309.13101/) (2023)
- [Real-time Photorealistic Dynamic Scene Representation and Rendering with 4D Gaussian Splatting](https://mlsanity.com/paper/2310.10642/) (2023)
- [SC-GS: Sparse-Controlled Gaussian Splatting for Editable Dynamic Scenes](https://mlsanity.com/paper/2312.14937/) (2023)
- [Transolver: A Fast Transformer Solver for PDEs on General Geometries](https://mlsanity.com/paper/2402.02366/) (2024)
- [4D-Rotor Gaussian Splatting: Towards Efficient Novel View Synthesis for Dynamic Scenes](https://mlsanity.com/paper/2402.03307/) (2024)
- [ReconX: Reconstruct Any Scene from Sparse Views with Video Diffusion Model](https://mlsanity.com/paper/2408.16767/) (2024)
- [Thermal3D-GS: Physics-induced 3D Gaussians for Thermal Infrared Novel-view Synthesis](https://mlsanity.com/paper/2409.08042/) (2024)
- [ThermalGaussian: Thermal 3D Gaussian Splatting](https://mlsanity.com/paper/2409.07200/) (2024)
- [ThermalNeRF: Thermal Radiance Fields](https://mlsanity.com/paper/2407.15337/) (2024)
- [TRACE: Learning 3D Gaussian Physical Dynamics from Multi-view Videos](https://mlsanity.com/paper/2508.09811/) (2025)
- [NTR-Gaussian: Nighttime Dynamic Thermal Reconstruction with 4D Gaussian Splatting Based on Thermodynamics](https://mlsanity.com/paper/2503.03115/) (2025)
- [Veta-GS: View-dependent deformable 3D Gaussian Splatting for thermal infrared Novel-view Synthesis](https://mlsanity.com/paper/2505.19138/) (2025)
- [Simultaneous temperature estimation and nonuniformity correction from multiple frames](https://mlsanity.com/paper/2307.12297/) (2023)
- [Virtual Temperature Sensors in Power Transformers Using Neural Ordinary Differential Equations](https://mlsanity.com/paper/2608.13260/) (2026)

## Abstract (arXiv)

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 rendering and future-time thermal-state prediction. Experiments on real infrared sequences and synthetic dynamic thermal data demonstrate improved reconstruction accuracy and substantially stronger temporal extrapolation than representative baselines, while also validating the applicability of GTSM to deforming targets.