{"title":"Data-Driven Reconstruction of a Low-Order Dynamo Model from Sunspot Data","authors":"Alfio Bonanno, Rainer Arlt","doi":"10.1007/s11207-025-02531-y","DOIUrl":null,"url":null,"abstract":"<div><p>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 <span>\\(B_{\\phi }\\dot{B}_{\\phi }^{2}\\)</span> 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.</p></div>","PeriodicalId":777,"journal":{"name":"Solar Physics","volume":"300 8","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11207-025-02531-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Solar Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11207-025-02531-y","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ASTRONOMY & ASTROPHYSICS","Score":null,"Total":0}
引用次数: 0
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 \(B_{\phi }\dot{B}_{\phi }^{2}\) 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.
了解太阳发电机的长期变化仍然是太阳物理学的一个关键挑战。在这项工作中,我们应用非线性动力系统的稀疏识别(SINDy)框架,直接从275年的太阳黑子数数据重建一个低阶发电机模型。我们从时间序列中发现控制方程的数据驱动方法使我们能够确定一个最小但准确的动力系统,该系统捕获了太阳活动周期的基本特征。我们证明,当解释为一个低阶发电机模型时,太阳能发电机是由一个不稳定的鞍点控制的,非线性演化导致循环行为。特别是,我们发现潜在的动力学是由\(B_{\phi }\dot{B}_{\phi }^{2}\)项驱动的三次非线性描述的,这导致相空间不一定属于Van der Pol普适类。此外,我们表明,高阶非线性是不利的,我们讨论了如何解释我们的发现在平均场发电机模型与一个新的淬火项。
期刊介绍:
Solar Physics was founded in 1967 and is the principal journal for the publication of the results of fundamental research on the Sun. The journal treats all aspects of solar physics, ranging from the internal structure of the Sun and its evolution to the outer corona and solar wind in interplanetary space. Papers on solar-terrestrial physics and on stellar research are also published when their results have a direct bearing on our understanding of the Sun.