Thermodynamic-Inspired Explainable GeoAI: Uncovering Regime-Dependent Mechanisms in Heterogeneous Spatial Systems

Modeling spatial heterogeneity and associated critical transitions remains a fundamental challenge in geography and environmental science. While conventional Geographically Weighted Regression (GWR) and deep learning models have improved predictive skill, they often fail to elucidate state-dependent nonlinearities where the functional roles of drivers represent opposing effects across heterogeneous domains. We introduce a thermodynamics-inspired explainable geospatial AI framework that integrates statistical mechanics with graph neural networks. By conceptualizing spatial variability as a thermodynamic competition between system Burden (E) and Capacity (S), our model disentangles the latent mechanisms driving spatial processes. Using three simulation datasets and three real-word datasets across distinct domains (housing markets, mental health prevalence, and wildfire-induced PM2.5 anomalies), we show that the new framework successfully identifies regime-dependent role reversals of predictors that standard baselines miss. Notably, the framework explicitly diagnoses the phase transition into a Burden-dominated regime during the 2023 Canadian wildfire event, distinguishing physical mechanism shifts from statistical outliers. These findings demonstrate that thermodynamic constraints can improve the interpretability of GeoAI while preserving strong predictive performance in complex spatial systems.

ZENN: A Thermodynamics-Inspired Computational Framework for Heterogeneous Data-Driven Modeling

Traditional entropy-based methods - such as cross-entropy loss in classification problems - have long been essential tools for quantifying uncertainty and disorder in data and developing artificial intelligence algorithms. However, the rapid growth of data across various domains has introduced new challenges, particularly the integration of heterogeneous datasets with intrinsic disparities. In this paper, we extend zentropy theory into the data science domain by introducing intrinsic entropy, enabling more effective learning from heterogeneous data sources. We propose a zentropy-enhanced neural network (ZENN) that simultaneously learns both energy and intrinsic entropy components, capturing the underlying structure of multi-source data. To support this, we redesign the neural network architecture to better reflect the intrinsic properties and variability inherent in diverse datasets. We demonstrate the effectiveness of ZENN on classification tasks and energy landscape reconstructions, showing its superior generalization capabilities and robustness-particularly in predicting high-order derivatives. As a practical application, we employ ZENN to reconstruct the Helmholtz energy landscape of Fe3Pt using data generated from DFT and capture key material behaviors, including negative thermal expansion and the critical point in the temperature-pressure space. Overall, our study introduces a novel approach for data-driven machine learning grounded in zentropy theory, highlighting ZENN as a versatile and robust deep learning framework for scientific problems involving complex, heterogeneous datasets.

Comparing Forward and Inverse Design Paradigms: A Case Study on Refractory High-Entropy Alloys

The rapid design of advanced materials is a topic of great scientific interest. The conventional, ``forward'' paradigm of materials design involves evaluating multiple candidates to determine the best candidate that matches the target properties. However, recent advances in the field of deep learning have given rise to the possibility of an ``inverse'' design paradigm for advanced materials, wherein a model provided with the target properties is able to find the best candidate. Being a relatively new concept, there remains a need to systematically evaluate how these two paradigms perform in practical applications. Therefore, the objective of this study is to directly, quantitatively compare the forward and inverse design modeling paradigms. We do so by considering two case studies of refractory high-entropy alloy design with different objectives and constraints and comparing the inverse design method to other forward schemes like localized forward search, high throughput screening, and multi objective optimization.