用数学方程从数据中学习可解释的气象模型
Learning Physically Interpretable Atmospheric Models from Data with WSINDy
- 基于弱形式稀疏非线性动力学，从数据中提取物理方程
- 在模拟与同化数据上均实现高精度气象建模
- 适合需要模型可解释性的气候研究者
地球大气的多尺度和湍流特性使精确天气建模长期面临挑战。近年来，数据驱动方法在天气预报中表现出更高的准确性和计算效率，但多数方法依赖高度参数化的神经网络，导致模型不可解释，科学理解有限。本文提出利用弱形式稀疏非线性动力学（WSINDy）算法，从模拟和同化数据中直接发现描述大气现象的偏微分方程，构建具有明确物理意义的符号化数学模型。该方法针对任意空间维度的高维流体数据进行了适配，证明了在实际气象数据上学习有效且可解释模型的可行性。
原文摘要 · Abstract (English)
The multiscale and turbulent nature of Earth's atmosphere has historically rendered accurate weather modeling a hard problem. Recently, there has been an explosion of interest surrounding data-driven approaches to weather modeling, which in many cases show improved forecasting accuracy and computational efficiency when compared to traditional methods. However, many of the current data-driven approaches employ highly parameterized neural networks, often resulting in uninterpretable models and limited gains in scientific understanding. In this work, we address the interpretability problem by explicitly discovering partial differential equations governing atmospheric phenomena, identifying symbolic mathematical models with direct physical interpretations. The purpose of this paper is to demonstrate that, in particular, the Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) algorithm can learn effective atmospheric models from both simulated and assimilated data. Our approach adapts the standard WSINDy algorithm to work with high-dimensional fluid data of arbitrary spatial dimension.
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