Collaborative Research: SHF: Small: Sub-millisecond Topological Feature Extractor for High-Rate Machine Learning

高速率系统被定义为经历高速率和高幅度事件的动态系统。例子包括高超声速飞行器和主动撞击缓解战略。这些机构的先进运行只能通过能够在亚毫秒范围内运行的控制和反馈系统来实现，因此需要严格的性能限制。此外，高速系统是高度非线性和非平稳的，传统的实时推理方法无法提供可靠的预测。拓扑数据分析在对复杂时间序列进行分类方面越来越受到人们的欢迎。它与构建的机器学习算法的集成显示出在提高高速率系统的预测能力方面的前景。然而，拓扑数据分析的计算成本很高，并且不能在亚毫秒范围内应用。该项目将通过发展和整合数学、软件和硬件基础方面的进步来研究实时拓扑数据分析能力。该项目的成功完成将为将拓扑数据分析与机器学习相结合以对时间序列进行建模和预测奠定理论基础，构成从纯代数拓扑法的重大飞跃。据设想，开发的基础以及软件和硬件制品将在超级计算、高速数据存储、联网车辆、金融欺诈缓解、网络安全、深度假冒检测、主动爆炸屏蔽和高超声速飞行器中得到应用。这个项目将通过一个结构良好的研究和教育计划来培训多名本科生和研究生，从而扩大对计算的参与。该计划利用三所合作大学的现有计划和合作伙伴关系，包括一所历史上一直是黑人的本科生大学。该项目将证明，通过将现代数学工具与硬件的进步相结合，可以实时学习复杂的非平稳系统，特别是通过为在边缘运行的实时预测器生成现场可编程门阵列设计。为此，将开发传统拓扑数据分析的定制变体，以满足目标建模和预测任务的需要，同时产生计算效率高的机器学习表示法。同时，将确定在进行实时拓扑数据分析和为不同硬件生产模块化自动化编程器方面的机会和限制。然后，将整合软件和硬件发现，以演示实时拓扑数据分析并进行时间序列建模和预测。参与这些研究项目的本科生将被提供长期的指导研究和学习经验。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。

High-rate systems are defined as dynamic systems experiencing high-rate and high-amplitude events. Examples include hypersonic vehicles and active impact mitigation strategies. The advanced operation of these mechanisms can only be achieved through control and feedback systems capable of operating in the sub-millisecond range, thus necessitating tight performance constraints. Additionally, high-rate systems are highly nonlinear and nonstationary, for which traditional real-time inference methods are incapable of providing credible predictions. Topological data analysis is gaining popularity for classifying complex time series. Its integration with architected machine learning algorithms shows promise in advancing the predictive capabilities for high-rate systems. However, topological data analysis is computationally expensive and cannot be applied in the sub-millisecond range. This project will investigate real-time topological data analysis capabilities by developing and integrating advances in mathematical, software, and hardware foundations. Successful completion of this project will yield theoretical foundations enabling the integration of topological data analysis with machine learning for modeling and forecasting time series, constituting a major leap from the pure algebraic topological approach. It is envisioned that the developed foundations, along with software and hardware artifacts, will find applications in supercomputing, high-speed data storage, connected vehicles, financial fraud mitigation, cyber-security, deep-fake detection, active blast shielding, and hypersonic vehicles. This project will broaden participation in computing by training multiple undergraduate and graduate students through a well-structured research and education plan that leverages existing programs and partnerships at the three partnering universities, including an undergraduate historically black college.This project will demonstrate that complex nonstationary systems can be learned in real-time by integrating modern mathematical tools combined with advances in hardware, notably by generating a field-programmable gate array design for a real-time predictor running on the edge. To that end, customized variations of traditional topological data analysis will be developed to meet the needs of the targeted modeling and forecasting tasks while producing computationally efficient machine learning representations. Concurrently, opportunities and limitations in conducting topological data analysis in real-time and in producing a modular automated programmer for heterogeneous hardware will be identified. Then, software and hardware discoveries will be integrated to demonstrate real-time topological data analysis and to conduct time series modeling and forecasting. Undergraduate students involved in these research projects will be provided with long-term mentored research and learning experiences.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.