用物理约束训练神经网络，精准预测地下储氢吸附行为。
Physics-Informed Neural Networks for Predicting Hydrogen Sorption in Geological Formations: Thermodynamically Constrained Deep Learning Integrating Classical Adsorption Theory
- 将经典吸附理论与热力学约束融入神经网络，提升跨岩性泛化能力。
- 测试集上达R2=0.954，误差仅0.0484 mmol/g，且无非物理解。
- 适合地质储氢评估、碳中和能源系统建模的研究者使用。
精确预测细粒度地质材料中的氢吸附对评估地下储氢容量、判断盖层完整性及刻画地下氢迁移至关重要。传统等温模型在单样本层面表现良好（R²=0.80-0.90），但在多样本聚合数据上性能骤降（R²=0.09-0.38）。本文提出一种多尺度物理信息神经网络框架，通过将经典吸附理论与热力学约束嵌入学习过程解决该问题。利用1,987条来自黏土、页岩、煤的氢吸附等温线数据，结合224条特征吸附量数据，构建62个热力学有意义的描述符。损失函数通过惩罚权重强制饱和极限、单调压力响应及Van't Hoff温度依赖性，并采用三阶段课程训练策略稳定整合冲突物理约束。由十名成员构成的架构异构集成模型提供校准的不确定性量化，后验温度校准实现目标置信区间覆盖率。优化后的PINN在保留测试集上达到R²=0.9544，RMSE=0.0484 mmol/g，MAE=0.0231 mmol/g，98.6%满足单调性，无非物理解。物理信息正则化在留一岩性排除验证中相较调优随机森林提升10-15%跨岩性泛化能力，证实热力学约束可有效跨地质边界迁移。
原文摘要 · Abstract (English)
Accurate prediction of hydrogen sorption in fine-grained geological materials is essential for evaluating underground hydrogen storage capacity, assessing caprock integrity, and characterizing hydrogen migration in subsurface energy systems. Classical isotherm models perform well at the individual-sample level but fail when generalized across heterogeneous populations, with the coefficient of determination collapsing from 0.80-0.90 for single-sample fits to 0.09-0.38 for aggregated multi-sample datasets. We present a multi-scale physics-informed neural network framework that addresses this limitation by embedding classical adsorption theory and thermodynamic constraints directly into the learning process. The framework utilizes 1,987 hydrogen sorption isotherm measurements across clays, shales, coals, supplemented by 224 characteristic uptake measurements. A seven-category physics-informed feature engineering scheme generates 62 thermodynamically meaningful descriptors from raw material characterization data. The loss function enforces saturation limits, a monotonic pressure response, and Van't Hoff temperature dependence via penalty weighting, while a three-phase curriculum-based training strategy ensures stable integration of competing physical constraints. An architecture-diverse ensemble of ten members provides calibrated uncertainty quantification, with post-hoc temperature scaling achieving target prediction interval coverage. The optimized PINN achieves R2 = 0.9544, RMSE = 0.0484 mmol/g, and MAE = 0.0231 mmol/g on the held-out test set, with 98.6% monotonicity satisfaction and zero non-physical negative predictions. Physics-informed regularization yields a 10-15% cross-lithology generalization advantage over a well-tuned random forest under leave-one-lithology-out validation, confirming that thermodynamic constraints transfer meaningfully across geological boundaries.
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