Data-Driven Reconstruction of a Low-Order Dynamo Model from Sunspot Data

Abstract Understanding the long-term variability of the solar dynamo remains a key challenge in solar physics. In this work, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework to reconstruct a low-order dynamo model directly from 275 years of sunspot number data. Our data-driven approach for discovering governing equations from time series enables us to identify a minimal yet accurate dynamical system that captures the essential features of solar activity cycles. We demonstrate that, when interpreted as a low-order dynamo model, the solar dynamo is governed by an unstable saddle point, with nonlinear evolution leading to cyclic behavior. In particular we find that the underlying dynamics is described by a cubic nonlinearity driven by a $B_{\phi }\dot{B}_{\phi }^{2}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>B</mml:mi> <mml:mi>ϕ</mml:mi> </mml:msub> <mml:msubsup> <mml:mover> <mml:mi>B</mml:mi> <mml:mo>˙</mml:mo> </mml:mover> <mml:mi>ϕ</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> term, which results in a phase space not necessarily of the Van der Pol universality class. Additionally, we show that higher-order nonlinearities are disfavored, and we discuss how to interpret our findings in terms of a mean-field dynamo model with a novel quenching term.