DMS-EPSRC Collaborative Research: Sharp Large Deviation Estimates of Fluctuations in Stochastic Hydrodynamic Systems

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Extreme events can be highly impactful. They are typically rare, which is fortunate if their consequences are negative on society, but also makes them difficult to predict. The focus of this project is to develop computational tools that can be applied to gain understanding of how extreme events occur in complex stochastic systems. Examples are models for the forecasting of extreme weather-related events like tropical storms and flooding as well as the spread of pollutants in case of ocean oil spills. These tools will enable researchers to ask questions beyond what is currently possible. This will lead to transformative improvement of current predictive models, which is essential for efficient management of natural and man-made disasters. Further applications include the characterization of extreme events in stochastic models that behave similar to fluids, for example in the context of epidemics, traffic, and star formation. This collaborative project will support one graduate student per year at NYU.Rare events are difficult to observe in controlled (numerical or physical) experiments, even for low-dimensional systems. The difficulty increases with the number of degrees of freedom, which makes high-dimensional systems even harder to analyze — fluids described by stochastic hydrodynamic models are a particular example of interest. As a result the questions that researchers can ask in order to gain insights about extreme events in these systems are often limited. The goal of this project is to analyze rare but important events in complex systems by developing new mathematical and computational tools to establish their most likely way of occurrence and calculate sharp asymptotic estimates (with prefactor included) of their probability and recurrence time. The aim is to create a toolbox applicable to a wide range of models with a large number of degrees of freedom described by stochastic partial differential equations (PDEs), like advection-diffusion equations and Navier-Stokes equations, and transferable across disciplinary borders. These tools will be applied to stochastic hydrodynamic systems in order to gain deeper insights of classical turbulence. In addition, the efficiency of this novel approach will be demonstrated in the context of real-world applications, in particular the advection of pollutants and the capsizing of ships.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.