Learning Physically Interpretable Atmospheric Models from Data with WSINDy
This addresses the need for interpretable models in atmospheric science, offering a method that balances accuracy with scientific understanding, though it is incremental as it builds on existing WSINDy techniques.
The paper tackles the interpretability problem in data-driven weather modeling by discovering partial differential equations governing atmospheric phenomena, resulting in physically interpretable models using the WSINDy algorithm adapted for high-dimensional fluid data.
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.