Harnessing the Data Revolution in Space Physics: Topological Data Analysis and Deep Learning for Improved Solar Eruption Prediction

太阳黑子——太阳可见表面的大量磁场——产生的火山爆发会对地球上的技术系统产生严重影响，破坏卫星和电网，以及其他许多东西。有了足够的提前通知，这些事件的影响可以减轻，但预测它们是一个真正的挑战。在目前的操作实践中，这是通过人类预报员检查太阳图像来完成的，根据20世纪60年代开发的分类法对每个太阳黑子进行分类，然后使用历史概率查找表来预测它是否会在未来24小时内爆发。最近，人们在机器学习方法上进行了大量工作，以使这项任务自动化。迄今为止，在这些方法中使用的“特征”主要是基于物理的：例如，磁场的梯度，或者在高通量区域上的强度总和。这个为期3年的研究项目的主要目标是利用基于形状基本数学（拓扑和几何）的算法来提高这些方法的性能。具体的计划是使用这些强大的技术来扩展相关的特征集，以包括纯粹基于二维磁图图像的几何和拓扑结构的磁场特征。虽然这种方法忽略了全电磁场的三维结构，但它可以提高机器学习系统的预测能力。初步结果显示，2017年太阳黑子在爆发前24小时的磁图中出现了明显的拓扑变化，并且利用这些基于形状的特征的基于神经网络的耀斑预测方法的精度得分明显提高。更好地预测太阳耀斑可以让电网、航空公司、通信卫星和其他关键基础设施系统的运营商减轻这些潜在破坏性事件的影响。该项目的更广泛影响还包括通过在科罗拉多大学博尔德分校培训研究生来发展STEM劳动力，以及教育和推广，包括社区讲座、开发大型在线课程和公共讲座系列。该项目的跨学科性质将加深空间天气、应用数学和计算机科学领域之间的联系，使这两个领域的研究人员、学生和博士后进入富有成效的新合作。与科罗拉多大学空间天气技术、研究和教育中心的合作提供了独特的机会，将现实世界的预测限制因素考虑在内，并为将结果转化为操作状态奠定了基础。这个为期3年的研究项目将首次为太阳耀斑预测提供系统的定量测量太阳光球中二维磁性结构的形状。从某种意义上说，这相当于对可敬的麦金托什和黑尔分类系统的数学系统化。这种方法不同于目前太阳物理学界对磁场线结构建模的研究：它使用拓扑学来解决二维集合的结构。分析仅限于光球磁场结构；目标是提取形状的正式特征，可以通过机器学习来改进耀斑预测。如果他们想要捕捉太阳黑子演化过程中重要结构的全部丰富性和物理相关性，项目团队考虑在这些方法中加入几何是必不可少的。该研究项目将为基于机器学习的火山爆发预测架构提供更强大的功能集。该项目的研究和EPO议程支持AGS部门在发现、学习、多样性和跨学科研究方面的战略目标。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Eruptions generated by sunspots --- large concentrations of magnetic field on the visible surface of the Sun --- can have a number of dire impacts on Earth-based technological systems, crippling satellites and power grids, among many other things. With enough advance notice, the effects of these events can be mitigated, but predicting them is a real challenge. In current operational practice, this is accomplished by human forecasters examining images of the Sun, classifying each sunspot according to a taxonomy developed in the 1960s, and then using look-up tables of historical probabilities to say whether or not it will erupt in the next 24 hours. Recently, there has been a burst of work on machine-learning methods to automate this task. To date, the "features" used in these approaches have been predominately physics-based: the gradient of the magnetic field, for instance, or the sum of its strength over high-flux regions. The main objective of this 3-year research project is to leverage algorithms based on the fundamental mathematics of shape --- topology and geometry --- to improve the performance of these methods. The specific plan is to use these powerful techniques to extend the relevant feature set to include characteristics of the magnetic field that are based purely on the geometry and topology of 2D magnetogram images. Although this approach ignores the 3D structure of the full electromagnetic fields, it can enhance the predictive skill of machine learning systems. Preliminary results show clear topological changes emerging in magnetograms of a 2017 sunspot more than 24 hours before it flared, as well as clear improvements in the accuracy scores of a neural-net based flare prediction method that employs these shape-based features. Better predictions of solar flares could allow operators of power grids, airlines, communications satellites, and other critical infrastructure systems to mitigate the effects of these potentially destructive events. The broader impacts of this project also include the development of the STEM workforce through the training of graduate students at the University of Colorado at Boulder, as well as education and outreach, including community lectures, development of large-scale, online courses and public lecture series. The interdisciplinary nature of the project will deepen the contact between the fields of space weather, applied mathematics, and computer science, bringing researchers, students, and post-docs from both fields into productive new collaborations. The collaboration with the Space Weather Technology, Research, and Education Center at the University of Colorado offers unique opportunities to factor in real-world forecasting constraints and set the stage for transitioning the results to operational status.For the first time, this 3-year research project would provide systematic quantitative measures of the shape of 2D magnetic structures in the Sun’s photosphere for the purposes of solar flare prediction. In a sense, this amounts to a mathematical systemization of the venerable McIntosh and Hale classification systems. This approach differs from current studies in the solar physics community that model the magnetic field-line structure: it uses topology to address the structure of two-dimensional sets. The analysis is restricted to photospheric magnetic field structures; the goal is to extract a formal characterization of shape that can be leveraged by machine learning to improve flare prediction. The considered addition of geometry into these methods by the project team is essential if they are to capture the full richness and physical relevance of the structures important in the evolution of a sunspot. This research project will point the way forward to a more robust set of features for machine-learning-based eruption prediction architectures. The research and EPO agenda of this project supports the Strategic Goals of the AGS Division in discovery, learning, diversity, and interdisciplinary research.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.