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

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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.