V. Kisielius | Searcharxiv

arXiv2026

Neural Differential Equations for the Solar Dynamo

Physical models aimed to reproduce basic features of the solar sunspot cycle are typically based on the solar dynamo mechanism. Usually qualitative arguments are used to define parameters of the model, among which a challenging component is the nonlinear form of quenching of the alpha-effect governing regeneration of the magnetic field. We propose a novel approach, in which the functional form of the alpha-quenching is represented by a neural network model embedded into neural differential dynamo equations trained on observational data. For demonstration, we consider a low-mode dynamo model and find a wide set of alpha-quenching functions and corresponding dynamo numbers that provide an accurate fit to the average profile of the solar cycle data given by sunspot numbers. Within this set, we observe a strong relationship between the dynamo number and the shape of the alpha-quenching function indicating that additional magnetic field data or constraints are essential to unambiguously infer parameters of the dynamo model. In our opinion, the neural differential approach opens a new prospect for data-driven investigation of the closure problem in dynamo theory.

astro-ph.SR↗

arXiv2024

Machine learning for reconstruction of polarity inversion lines from solar filaments

Solar filaments are well-known tracers of polarity inversion lines that separate two opposite magnetic polarities on the solar photosphere. Because observations of filaments began long before the systematic observations of solar magnetic fields, historical filament catalogs can facilitate the reconstruction of magnetic polarity maps at times when direct magnetic observations were not yet available. In practice, this reconstruction is often ambiguous and typically performed manually. We propose an automatic approach based on a machine-learning model that generates a variety of magnetic polarity maps consistent with filament observations. To evaluate the model and discuss the results we use the catalog of solar filaments and polarity maps compiled by McIntosh. We realize that the process of manual compilation of polarity maps includes not only information on filaments, but also a large amount of prior information, which is difficult to formalize. In order to compensate for the lack of prior knowledge for the machine-learning model, we provide it with polarity information at several reference points. We demonstrate that this process, which can be considered as the user-guided reconstruction or super-resolution, leads to polarity maps that are reasonably close to hand-drawn ones, and additionally allows for uncertainty estimation.

cs.LG↗