Disturbance storm time index prediction with interpretable machine learning

The Disturbance Storm Time (Dst) index quantifies geomagnetic storm intensity by measuring global magnetic field variations. In this study, we apply interpretable machine-learning (ML) techniques to derive data-driven models 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. We employ KAN networks and the symbolic regression framework PyOperon , based on an evolutionary algorithm, to identify closed-form expressions linking d Dst / d t to key solar wind parameters. The equations obtained via symbolic regression form a hierarchy of complexity levels and capture nonlinear dependencies and threshold effects in Dst evolution. In addition, we use a conventional MLP network as a reference black-box model. We benchmark all ML models against observed Dst data and compare their performance with empirical formulations such as the Burton-McPherron–Russell and O’Brien-McPherron models. The performance evaluation on historical storm events includes the 2003 Halloween storm, the 2015 St. Patrick’s Day storm, a moderate storm in 2017, and the extreme storm of May 2024. The data-driven models, particularly the MLP, demonstrate superior accuracy in most cases. While the symbolic regression expressions provide insight into the underlying physics, the results highlight an intrinsic trade-off between model interpretability and predictive accuracy. This is an extended version of a previous work presented in Markidis et al. (2025) 1 . • We design the state-of-the-art interpretable machine learning methodologies, such as symbolic regression and Kolmogorov–Arnold Networks, for space weather applications. We derive data-driven models for predicting the Dst temporal evolution, compare them to black-box methods, such as multi-perceptron neural networks in terms of accuracy. • We identify a hierarchy of data-driven symbolic regression models, obtained with the Operon framework, by varying equation complexity as input to Operon . We recover equations with progressively richer physical content and increasing accuracy. • We compare the discovered equations with well-established magnetospheric physics empirical models, such as the Burton-McPherron-Russell (Burton et al., 1975) and O’Brien-McPherron models (O’Brien et al., 2000, 2022), in accuracy. We show that the best models found with the symbolic regression approach outperform these established models in the cases considered. • We show that the Multi-Layer-Perceptron black-box approach outperforms the empirical and derived equations, especially for extreme events. Highlighting the complex dynamics in the Earth’s magnetosphere and the cost of simplified models.