Physics-Informed-ML: Soil Moisture Prediction with PINNs

📌 Context & Overview

Traditional Deep Learning models often act as "black boxes," ignoring the fundamental laws of physics. In eco-hydrology, soil moisture dynamics follow mass conservation principles. This project explores the implementation of Physics-Informed Neural Networks (PINNs) to predict the Normalized Difference Water Index (NDWI) while integrating water mass balance constraints into the loss function.

🎯 Objectives

• Hybrid Modeling: Combining data-driven learning (satellite indices) with physical constraints (water conservation).
• PINN Implementation: Developing a custom loss function that penalizes predictions violating hydrological laws.
• Experimental Benchmarking: Assessing the stability of neural networks when forced to respect physical boundaries.

🛠️ Tech Stack & Methodology

• Language/Platform: Python (Google Colab).
• Deep Learning: TensorFlow or PyTorch (Fully Connected Architecture).
• Physics Integration: Custom Loss Function defined as: $$Loss_{total} = MSE_{data} + \lambda_{phys} \cdot MSE_{physics}$$
• Parameters: Input features include LST (Temperature), NDVI (Vegetation), and Precipitation for 313 sub-basins.

🚀 Experimental Insights & Results

• The PINN Challenge: The model faced stability issues, highlighting the difficulty of balancing data accuracy with physical consistency in complex environmental systems.
• Model Diagnostics: Predictions showed an underestimation of NDWI, likely due to a simplified formalization of the water balance equation ($\Delta W \approx P - ET$).
• Critical Learning: The project demonstrated that PINNs require highly calibrated datasets and precise mathematical definitions of physical residuals to converge effectively.
• Methodological Value: Despite the convergence hurdles, the experiment provides a foundational framework for integrating Earth Observation data with differential equations in Python.

🔮 Perspectives for Improvement

• Refined Formalization: Improving the Evapotranspiration (ET) estimation using LST and NDVI through Penman-Monteith derived proxies within the network.
• Architectural Search: Testing Recurrent Neural Networks (LSTM-PINN) to better capture the temporal memory of soil moisture.
• Data Normalization: Implementing more robust scaling techniques to align disparate satellite and climatic variables.
• Dynamic Penalization: Using self-adaptive weights ($\lambda_{phys}$) to balance the loss terms during training epochs.

Link https://colab.research.google.com/drive/1XuZI-yg0GKGwTNFyXmstVwE0xU9Co3UA