Collaborative Research: Construction and Analysis of Numerical Methods for Stochastic Inverse Problems with Application to Coastal Hydrodynamics

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As observed in past hurricanes such as Katrina (2005), Ike (2008), Sandy (2012), and the sequence of hurricanes over the 2017 season, flooding due to storm surge and rainfall causes tremendous damage to coastal communities. Preparing for future hurricane impacts requires the ability to predict characteristics of inland flooding due to surge, most importantly water levels, currents, and extent of inundation. Accurate predictions of surge require determining critical inputs to models related to the physical characteristics of coastal regions that are expensive to obtain and evolve in time. This research project focuses on quantifying and reducing uncertainties in these critical inputs using novel mathematical techniques to both extract information from existing data and aid in the design of future data collection efforts.More specifically, this project focuses on the construction, analysis, and implementation of numerical methods for a stochastic inverse problem defined by the melding of observational data and high-fidelity mathematical models to perform scientific and engineering inference and prediction for complex physical systems. This research applies broadly to complex, time-evolving physical systems depending on high dimensional parameter spaces. Mathematical areas utilized in this research include computational measure theory, differential geometry, functional analysis, probability theory, and numerical analysis. Dissemination of results to the broader scientific community will be accomplished in part by the development and implementation of computational algorithms in public domain code that are applied to a state-of-the-art storm surge model.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.