用物理约束提升甲烷吸附预测，实现跨气种迁移学习与精准不确定性评估。
Physics-Informed Neural Networks for Methane Sorption: Cross-Gas Transfer Learning, Ensemble Collapse Under Physics Constraints, and Monte Carlo Dropout Uncertainty Quantification
- 基于弹性权重固化与分阶段课程学习，实现氢气预训练向甲烷预测的高效迁移。
- 在993组数据上达R²=0.932，性能比传统模型高227%，收敛快19.4%。
- 蒙特卡洛丢弃法表现最优，适合地质材料建模中需物理可解释性的场景。
跨异质煤阶准确预测甲烷吸附需兼顾热力学一致性、数据稀缺地质系统间的高效知识迁移及校准的不确定性估计，而现有框架极少同时满足三者。本文提出一种物理信息迁移学习框架：通过弹性权重固化、煤类特征工程与三阶段渐进式课程学习，将氢气吸附的物理信息神经网络（PINN）迁移至甲烷预测。在覆盖褐煤到无烟煤的114个独立实验共993组平衡数据上，模型在保留样本上取得R²=0.932，较仅依赖压力的经典等温线提升227%；氢气预训练使均方根误差降低18.9%，收敛速度加快19.4%。五种贝叶斯不确定性量化方法显示，物理约束架构下性能存在系统性差异：蒙特卡洛丢弃法在极小计算开销下实现良好校准，而深度集成无论结构多样性或初始化策略如何，均因共享物理约束缩小解空间导致性能下降。SHAP与ALE分析证实，学习表征保持物理可解释性：水分-挥发物相互作用影响最大，压温耦合捕捉热力学共依赖性，特征呈现非单调效应。结果表明，蒙特卡洛丢弃是该框架中最优的不确定性量化方法，并验证跨气种迁移学习为地质材料建模的高效策略。
原文摘要 · Abstract (English)
Accurate methane sorption prediction across heterogeneous coal ranks requires models that combine thermodynamic consistency, efficient knowledge transfer across data-scarce geological systems, and calibrated uncertainty estimates, capabilities that are rarely addressed together in existing frameworks. We present a physics-informed transfer learning framework that adapts a hydrogen sorption PINN to methane sorption prediction via Elastic Weight Consolidation, coal-specific feature engineering, and a three-phase curriculum that progressively balances transfer preservation with thermodynamic fine-tuning. Trained on 993 equilibrium measurements from 114 independent coal experiments spanning lignite to anthracite, the framework achieves R2 = 0.932 on held-out coal samples, a 227% improvement over pressure-only classical isotherms, while hydrogen pre-training delivers 18.9% lower RMSE and 19.4% faster convergence than random initialization. Five Bayesian uncertainty quantification approaches reveal a systematic divergence in performance across physics-constrained architectures. Monte Carlo Dropout achieves well-calibrated uncertainty at minimal overhead, while deep ensembles, regardless of architectural diversity or initialization strategy, exhibit performance degradation because shared physics constraints narrow the admissible solution manifold. SHAP and ALE analyses confirm that learned representations remain physically interpretable and aligned with established coal sorption mechanisms: moisture-volatile interactions are most influential, pressure-temperature coupling captures thermodynamic co-dependence, and features exhibit non-monotonic effects. These results identify Monte Carlo Dropout as the best-performing UQ method in this physics-constrained transfer learning framework, and demonstrate cross-gas transfer learning as a data-efficient strategy for geological material modeling.
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