Analytically Tractable Strategies for Modeling Extreme Events and Anomalous Statistics in Turbulent Multiscale Systems
Abstract
Project Summary/Abstract(Approved for Public Release)Understanding the fascinating phenomena of extreme events and the associated anomalous statistics observed in a wide variety of natural and engineering systems remains a grand challenge in contemporary mathematical and computational research with important societal impact. The emergence of such extreme features in diverse complex systems can be attributed to turbulent dynamics, characterized by intricate multiscale nonlinear interactions which redistribute energy acrossa wide spectrum of high-dimensional stable and unstable modes, ultimately leading to a complicated statistical equilibrium distinguished by non-Gaussian probability distributions. Key issues remains in understanding the basic mathematical properties for general turbulent systems involving multiscale structures, and qualitative prediction of crucial features with uncertainty quantification, data assimilation and control. Strategies for reduced nonlinear closure models, inspired by the pioneering work of Andrew Majda and recently developed by the PI, Di Qi, integrate ideas from stochastic modeling, rigorous mathematical theories, and innovative data-driven methods in an emerging paradigm for these grand challenges, particularly in extreme event prediction.The aim of this proposed project is to innovate novel theoretically tractable strategies capable of comprehending and quantifying complex extreme phenomena that are too rare to be easily detected and too impactful to be simply overlooked. The PI proposes to explore several facets of modeling and analyzing extreme events under a unified mathematical multiscale modeling framework. By employing a suitable theoretically tractable model reduction strategy, a systematic investigation will be conducted encompassing rigorous theoretical analysis, efficient computational algorithms, and practical applications to address pressing real-world problems. These overall objectives of the proposal will be pursued with the following expected outcomes concerning different interconnected aspects of the problem:#developing an analytically tractable modeling strategy for a systematic theoretical study of multiscale complex turbulent systems involving extreme phenomena and high-order statistics;#constructing computationally efficient state estimation and data assimilation algorithms for effective probability forecast coping with key non-Gaussian and irreducible multiscale structures;#designing advanced numerical solvers combining mathematical theory and computational tools for understanding crucial phenomena in practical problems.To achieve the objectives, the novel mathematical framework will be first used to design precise model reduction strategies for state and parameter estimation of crucial complex phenomena such as extreme weather events, transition in ocean waves, and turbulent transport across coherent vortices in plasma waves that could impact Naval strategic planning and enhance operational capabilities. New skillful numerical schemes will then be constructed to address key challenges in efficient prediction of the extreme probability with demanding computational cost in high dimensions. A hierarchical set of prototype benchmark systems with increasing complexity and particular structures of universal interests will be used for theoretical analysis and computational verification of the proposed reduced-order models and algorithms. Finally, new practical strategies will be devised for realistic applications coping with various practical challenges drawn from atmosphere and ocean and plasma systems. The new theoretically consistent modeling strategy and the concise computational algorithms derived from the mathematical framework will foster a synthesis of novel ideas and techniques from mathematics, statistics, physics and numerical analysis as well as many other related fields closely related to the interests of DoD and Navy.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Mar 08, 2024
- Source ID
- N000142412192
Entities
People
- Di Qi
Organizations
- Office of Naval Research
- Purdue University
- United States Navy