Machine Learning Methods for Thermodynamic Energy Flow Pattern Prediction at Regional Scales with High-Dimensional Climate Data

Accurate prediction of regional-scale thermodynamic energy flow patterns is crucial for understanding surface-atmosphere interactions and optimizing climate model parameterization schemes, playing a vital role in climate simulation and ecological environmental assessment.Traditional physics-guided machine learning (PGML) methods typically embed physical laws as fixed soft constraints in the model, which struggle to adapt to the spatiotemporal heterogeneity of key thermodynamic parameters under complex underlying surfaces and non-uniform conditions.This limitation affects the quantification accuracy of core parameters such as turbulence exchange coefficients and surface impedance.In this paper, we propose a dual-path physics-data hybrid framework that integrates the physical skeleton with data-driven dynamics through a collaborative architecture of differentiable physical kernels and spatiotemporal neural parameterization.The framework constructs a differentiable forward physics simulator based on discretized regional energy balance equations, while utilizing high-dimensional spatiotemporal encoder-decoder networks to adaptively generate grid-scale physical parameter fields from multi-source climate data.Combined with a multi-objective progressive learning strategy, the model achieves pre-training of parameters and physics-enhanced training.A closedloop integration module is used for energy flow evolution scenario simulation and uncertainty quantification.This model demonstrates significant predictive advantages across various spatial and temporal scales, as well as extreme weather scenarios.For instance, the daily-scale sensible heat flux in homogeneous farmland reduces mean squared error (MSE) by 38.7% compared to traditional PGML and 30.8% compared to Convolutional Neural Network-Long Short-Term Memory (CNN-LSTM), with an accuracy degradation rate of only 13.5%-17.3%under extreme scenarios.The energy conservation error is ≤ 5.7 W•m⁻².Ablation experiments validate the core role of innovative components such as the neural parameterization, while revealing a regional thermodynamic parameterization formula (R² = 0.89) for multi-surface adaptation, uncovering the differences in energy flow driving mechanisms across regions.This study upgrades machine learning from a traditional predictive tool to a mechanism discovery and model enhancement tool, offering new methods for improving regional thermodynamic parameterization schemes and enhancing the reliability of energy flow predictions in extreme scenarios.It holds significant academic value and practical prospects.