标题： 从数据中使用WSINDy学习具有物理可解释性的大气模型 显示英文标题

标题： Learning Physically Interpretable Atmospheric Models from Data with WSINDy

摘要： 地球大气的多尺度和湍流特性历史上使得准确的天气建模成为一个困难的问题。 最近，数据驱动的天气建模方法引起了广泛关注，在许多情况下，与传统方法相比，这些方法显示出更高的预测精度和计算效率。 然而，许多当前的数据驱动方法使用高度参数化的神经网络，通常导致不可解释的模型，并且在科学理解上的收益有限。 在这项工作中，我们通过显式发现控制大气现象的偏微分方程，识别具有直接物理解释的符号数学模型来解决可解释性问题。 本文的目的是证明，特别是弱形式稀疏非线性动力学识别（WSINDy）算法可以从模拟和同化数据中学习有效的大气模型。 我们的方法适应了标准的WSINDy算法，使其能够处理任意空间维度的高维流体数据。 显示英文摘要

摘要： 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.