Learning Weather Models from Data with WSINDy

2025-01-01

AI Summary

Weather forecasting faces a fundamental trade-off between predictive accuracy and model interpretability: data-driven models lack physical transparency, while physics-based models struggle to represent multiscale turbulent dynamics. To address this, we propose an interpretable modeling framework grounded in atmospheric dynamics. Specifically, we adapt the Weak-form Sparse Identification of Nonlinear Dynamics (WSINDy) method to high-dimensional fluid data for the first time, introducing a novel variational weak-form strategy to rigorously handle non-integrable-by-parts terms—such as advection—common in geophysical flows. By synergistically integrating high-fidelity numerical simulations and reanalysis assimilation data, our approach performs symbolic regression directly from observational data to recover physically meaningful partial differential equations. It successfully reconstructs Navier–Stokes–type evolution equations governing atmospheric dynamics. The resulting model achieves competitive forecast accuracy while yielding verifiable, interpretable dynamical mechanisms—thereby enhancing scientific transparency and theoretical insight in weather modeling.

Technology Category

• Machine Learning: Transparent, Interpretable, Explainable ML
• Natural Language Processing: Interpretability, Analysis, and Evaluation of NLP Models
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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 various weather 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 weather 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. Moreover, we develop an approach for handling terms that are not integrable-by-parts, such as advection operators.

Problem

• Explainable Rules
• Weather Prediction
• Data-Driven Models

Innovation

• WSINDy
• Weather Prediction
• Interpretable Models