Wang et al. (2026) A thermodynamics-integrated physics-guided neural network for soil temperature forecasting

Identification

• Journal: Scientific Reports
• Year: 2026
• Date: 2026-05-11
• Authors: Shengyi Wang, Jinlong Zhu
• DOI: 10.1038/s41598-026-50274-y

Research Groups

• College of Computer Science and Technology, Changchun Normal University, China.

Short Summary

The study develops a Thermodynamic-Enhanced Physics-Informed Neural Network (TE-PINN) that integrates thermodynamic priors into an LSTM framework to improve the accuracy and physical consistency of soil temperature forecasting. The model effectively reduces error accumulation in long-term predictions and enhances spatial generalization across different latitudes.

Objective

• To address the limitations of standard deep learning models in soil temperature forecasting, specifically error accumulation during long-term predictions, lack of physical interpretability, and poor spatial generalization.

Study Configuration

• Spatial Scale: Multi-latitude datasets (specific geographic coordinates not provided).
• Temporal Scale: Multi-day forecast horizons.

Methodology and Data

• Models used: Thermodynamic-Enhanced Physics-Informed Neural Network (TE-PINN), which consists of:
  • An LSTM backbone for temporal dependencies.
  • Latent Thermodynamic Potential Inference (LTPI) module (utilizing free-energy principles and dissipation constraints).
  • Multi-Pathway Physics-Guided Loss Integration (MPPGLI) module.
• Data sources: Soil temperature datasets from various latitudes (specific source names not provided in the text).

Main Results

• Improved Long-term Stability: TE-PINN exhibits slower performance degradation over multi-day forecast horizons compared to baseline models.
• Spatial Robustness: The model maintains stable predictive behavior across datasets from different latitudes.
• Enhanced Accuracy: The integration of thermodynamic priors significantly improves both the quantitative accuracy and the physical consistency of the forecasts relative to shallow and deep baseline models.

Contributions

• Proposes a novel framework (TE-PINN) that bridges the gap between data-driven LSTM models and thermodynamic laws.
• Introduces the LTPI and MPPGLI modules to incorporate dissipation constraints and free-energy principles, providing a method to constrain neural network outputs within physically plausible bounds.

Funding

• Natural Science Foundation of Changchun Normal University, No. CSJJ2023013ZK.

Citation

@article{Wang2026thermodynamicsintegrated,
  author = {Wang, Shengyi and Zhu, Jinlong},
  title = {A thermodynamics-integrated physics-guided neural network for soil temperature forecasting},
  journal = {Scientific Reports},
  year = {2026},
  doi = {10.1038/s41598-026-50274-y},
  url = {https://doi.org/10.1038/s41598-026-50274-y}
}