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

太阳黑子产生的喷发--太阳可见表面的大密度磁场--可能会对地球上的技术系统产生一些可怕的影响，使卫星和电网瘫痪，以及其他许多事情。如果事先得到足够的通知，这些事件的影响可以得到缓解，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，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询表来判断它是否会在未来24小时内爆发来完成的。最近，在机器学习方法方面已经有了大量的工作来自动完成这项任务。到目前为止，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，或其在高通量区域的强度总和。这个为期3年的研究项目的主要目标是利用基于基本形状数学-拓扑学和几何学--的算法来提高这些方法的性能。具体计划是使用这些强大的技术来扩展相关特征集，以包括纯粹基于2D磁图图像的几何和拓扑的磁场特征。虽然这种方法忽略了整个电磁场的三维结构，但它可以提高机器学习系统的预测能力。初步结果显示，2017年太阳黑子爆发前超过24小时的磁图中出现了明显的拓扑变化，使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分数也有了明显的提高。对太阳耀斑的更好预测可以让电网、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培训科罗拉多大学博尔德分校的研究生发展STEM工作队伍，以及教育和外联，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气象、应用数学和计算机科学领域之间的联系，将这两个领域的研究人员、学生和博士后带入富有成效的新合作中。与科罗拉多大学空间气象技术、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，并为将结果过渡到运行状态奠定了基础。这一为期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层2D磁结构的形状。在某种意义上，这相当于将历史悠久的麦金托什和黑尔分类系统在数学上系统化。这种方法不同于目前太阳物理界对磁场线结构进行建模的研究：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；其目标是提取可被机器学习用于改进耀斑预测的形状的形式特征。如果要捕捉太阳黑子演化中重要的结构的全部丰富性和物理相关性，项目团队考虑将几何学添加到这些方法中是必不可少的。这一研究项目将为基于机器学习的喷发预测体系结构提供一组更健壮的功能。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NSF的法定使命，并通过使用基金会的智力优势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.