ATD: A model-assisted data-driven framework for prediction of rare extreme events from sparse measurements

Rare extreme events, such as tsunamis, oceanic rogue waves, wildfires, and earthquakes, cause immense human, environmental, and financial damage. Yet, their effective prediction, quantification, and mitigation remains a major challenge. This project develops a synergistic framework for accurate and real-time prediction of rare extreme events using both observational data and mathematical models. The resulting methods will increase the accuracy of predictions based on available observational data. At the same time, they will significantly reduce the computational cost, making real-time predictions feasible. This project will also provide research training opportunities for graduate students.The evolution of spatiotemporal systems, such as fluid flows and waves, is described by partial differential equations (PDEs). High-resolution numerical simulations of these PDE models are valuable since they provide detailed information about the system and its dynamics. However, their high computational cost renders them ineffective for making real-time predictions. More importantly, the PDE models require detailed spatial measurements of the system which are often unattainable in practice where system observations are limited to a relatively small number of sensor locations. The objective of this project is to determine the optimal location of the sensors in order to enable accurate and real-time prediction of extreme events. The framework consists of two phases: (1) First, offline PDE simulations are leveraged to identify the optimal sensing locations and to machine learn a reliable indicator of extreme events. (2) Optimal real-time measurements and the pre-trained machine learning algorithm are used to predict future extreme events. Phase 1 is computationally expensive but is carried out offline and only once. The results are used in phase 2 in order to make fast real-time predictions with minimal computational cost. As such, the final results will increase the accuracy of extreme event prediction while decreasing its computational cost.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.