Learning Physically Interpretable Atmospheric Models from Data with WSINDy

TL;DR

This paper demonstrates that the WSINDy algorithm can learn interpretable, physics-based atmospheric models from high-dimensional data, improving understanding of atmospheric dynamics while maintaining forecasting accuracy.

Contribution

The paper adapts the WSINDy algorithm for high-dimensional atmospheric data, enabling the discovery of physically interpretable PDE models from complex fluid datasets.

Findings

WSINDy successfully learns atmospheric PDE models from simulated data.

The method provides interpretable models with physical significance.

Applicable to high-dimensional fluid data of arbitrary spatial dimensions.

Abstract

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.