用物理约束神经微分方程模拟积雪变化，精度高且可泛化。
A Physics-Constrained Neural Differential Equation Framework for Data-Driven Snowpack Simulation
- 结合物理规律的神经微分方程，学习积雪演变规律。
- 多站点训练后日尺度预测误差低于9%，效率超0.94。
- 支持不同时间分辨率建模，适合气候模拟与复杂系统。
本文提出一种物理约束的神经微分方程框架，用于参数化季节性积雪深度的时间演化，输入为水文气象强迫。在多个SNOTEL站点数据上训练后，该参数化对日尺度雪深预测的中位误差低于9%，纳什-萨特效率超过0.94，适用于多种积雪气候。模型还能泛化到训练未见的新站点，而传统校准模型常无法做到。若额外预测雪水当量，误差仅增至约12%。该方法结构保证物理约束满足，训练过程融入物理规则，并支持不同时间分辨率建模，无需重新训练。这些优势在气候模拟中有潜力，亦可扩展至其他具物理约束的动力系统。
原文摘要 · Abstract (English)
This paper presents a physics-constrained neural differential equation framework for parameterization, and employs it to model the time evolution of seasonal snow depth given hydrometeorological forcings. When trained on data from multiple SNOTEL sites, the parameterization predicts daily snow depth with under 9% median error and Nash Sutcliffe Efficiencies over 0.94 across a wide variety of snow climates. The parameterization also generalizes to new sites not seen during training, which is not often true for calibrated snow models. Requiring the parameterization to predict snow water equivalent in addition to snow depth only increases error to ~12%. The structure of the approach guarantees the satisfaction of physical constraints, enables these constraints during model training, and allows modeling at different temporal resolutions without additional retraining of the parameterization. These benefits hold potential in climate modeling, and could extend to other dynamical systems with physical constraints.
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