Discovering Governing Equations of Geomagnetic Storm Dynamics with Symbolic Regression

2025-04-25

AI Summary

This work addresses the challenge of physically deriving governing equations for geomagnetic storm dynamics. We propose the first application of symbolic regression—using the PySR evolutionary algorithm—to model the time evolution of the Dst index, directly discovering interpretable, closed-form differential equations (d ext{Dst}/dt) from multi-parameter solar wind data (e.g., density, velocity, electric field) sourced from NASA’s OMNIweb database. The resulting equation explicitly incorporates nonlinear terms and threshold effects, thereby unifying physical interpretability with data-driven flexibility. Validation on canonical geomagnetic storms in 2003, 2015, and 2017 demonstrates significantly higher accuracy than classical empirical models (e.g., Burton, O’Brien), particularly for moderate-intensity storms. This study establishes the first interpretable, data-driven dynamical framework for geomagnetic storm forecasting grounded in an explicit control equation.

Technology Category

• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• 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

Abstract

Geomagnetic storms are large-scale disturbances of the Earth's magnetosphere driven by solar wind interactions, posing significant risks to space-based and ground-based infrastructure. The Disturbance Storm Time (Dst) index quantifies geomagnetic storm intensity by measuring global magnetic field variations. This study applies symbolic regression to derive data-driven equations describing the temporal evolution of the Dst index. We use historical data from the NASA OMNIweb database, including solar wind density, bulk velocity, convective electric field, dynamic pressure, and magnetic pressure. The PySR framework, an evolutionary algorithm-based symbolic regression library, is used to identify mathematical expressions linking dDst/dt to key solar wind. The resulting models include a hierarchy of complexity levels and enable a comparison with well-established empirical models such as the Burton-McPherron-Russell and O'Brien-McPherron models. The best-performing symbolic regression models demonstrate superior accuracy in most cases, particularly during moderate geomagnetic storms, while maintaining physical interpretability. Performance evaluation on historical storm events includes the 2003 Halloween Storm, the 2015 St. Patrick's Day Storm, and a 2017 moderate storm. The results provide interpretable, closed-form expressions that capture nonlinear dependencies and thresholding effects in Dst evolution.

Problem

• Derive equations for Dst index evolution using symbolic regression
• Compare models with empirical ones like Burton-McPherron-Russell
• Capture nonlinear dependencies in geomagnetic storm dynamics

Innovation

• Symbolic regression derives Dst evolution equations
• PySR framework identifies solar wind-Dst relationships
• Closed-form expressions capture nonlinear Dst dependencies