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

罕见的极端事件，如海啸、海洋巨浪、野火和地震，会造成巨大的人类、环境和经济损失。然而，如何有效地预测、量化和缓解这些风险仍然是一个重大挑战。该项目开发了一个协同框架，利用观测数据和数学模型对罕见的极端事件进行准确和实时的预测。由此产生的方法将提高基于现有观测数据的预测的准确性。与此同时，它们将显著降低计算成本，使实时预测变得可行。本计画也将提供研究训练机会给研究生。时空系统的演化，例如流体流动与波，是用偏微分方程式来描述。这些PDE模型的高分辨率数值模拟是有价值的，因为它们提供了有关系统及其动力学的详细信息。然而，它们的高计算成本使它们无法进行实时预测。更重要的是，PDE模型需要详细的空间测量的系统，这往往是无法实现的，在实践中，系统的观察是有限的，相对较少的传感器位置。该项目的目标是确定传感器的最佳位置，以便能够准确和实时地预测极端事件。该框架包括两个阶段：（1）首先，利用离线PDE模拟来确定最佳感测位置并机器学习极端事件的可靠指标。(2)最佳实时测量和预先训练的机器学习算法用于预测未来的极端事件。阶段1在计算上是昂贵的，但是离线执行并且仅执行一次。结果用于第2阶段，以便以最小的计算成本进行快速实时预测。因此，最终结果将提高极端事件预测的准确性，同时降低其计算成本。该奖项反映了NSF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。

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.