Physics-Embedded Deep Learning for Wildfire Risk Assessment: Integrating Statistical Mechanics Into Neural Networks for Interpretable Environmental Modeling

Abstract This paper introduces a groundbreaking framework that fuses physical laws from statistical mechanics with deep learning to advance wildfire risk assessment. At its core is the "Physics-Embedded Entropy Layer," which adapts the Boltzmann-Gibbs entropy formula to measure landscape complexity and wildfire susceptibility using tabular environmental data. Integrated as a trainable middle layer within a Parallel Multi-path Feed Forward Neural Network (PMFFNN), this layer transforms raw inputs—such as vegetation indices, soil moisture, and meteorological data from the "Morocco Wildfire Predictions: 2010-2022 ML Dataset"—into an interpretable, physically grounded representation. A hybrid training approach, combining pretraining of the entropy layer with end-to-end fine-tuning, enables the model to achieve competitive precision and AUC scores, affirming its potential for reliable early warning systems. Although its overall accuracy is moderate compared to some data-driven baselines, the model’s balanced error profile and physical interpretability make it especially suitable for applications demanding trust and mechanistic insight. Beyond wildfires, this physics-embedded deep learning approach offers a scalable, interpretable paradigm for diverse scientific challenges, including climate modeling, material science, and environmental risk analysis, laying a robust foundation for future advancements in scientific machine learning.