Neural Differential Equations for the Solar Dynamo

TL;DR

This paper introduces a neural differential equation approach to model the solar dynamo, using neural networks to learn the nonlinear alpha-quenching function from observational sunspot data, enhancing data-driven understanding of solar magnetic activity.

Contribution

It presents a novel neural differential dynamo model that learns the alpha-quenching function directly from data, offering a new method for solar dynamo modeling and analysis.

Findings

Neural network-based alpha-quenching functions fit solar cycle data accurately.

A strong relationship exists between dynamo number and alpha-quenching shape.

Additional magnetic data are needed for unambiguous parameter inference.

Abstract

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.