Reduced Order Models, Prediction, and State Estimation for Complex Systems
Abstract
Complex multiscale nonlinear stochastic dynamical systems are ubiquitous complex systems in geoscience, engineering, neural and material sciences. They are a grand challenge in contemporary science and engineering.Key issues are their basic mathematical structural properties and qualitative features, their statistical prediction, uncertainty quantification (UQ) and sensitivity, their data assimilation (also known as state estimation or filtering), and coping with the inevitable model errors that arise in approximating such complex systems. These model errors arise through both the curse of small ensemble size for large systems and the lack of physical understanding.Strategies for effective reduced nonlinear stochastic models, recently developed by the PI, Majda, and co-workers, blend ideas from information theory, Bayesian statistics, and statistical physics in an emerging paradigm for these grand challenges, including extreme event prediction.The ~modus operandi~ of the proposed research effort is through the modern applied mathematics paradigm where rigorous mathematical theory, asymptotic/qualitative models, and novel numerical algorithms are all blendedtogether interactively to give insight into complex physical problems. This approach will be utilized in several main research directions proposed below:A) Improving Prediction Skill of Reduced-Order Forced Imperfect Turbulent Dynamical Systems through StatisticalResponse Theory and Information Theory;B) Novel Algorithms for Multi-scale Data Assimilation in Complex Turbulent Systems;C) Information Barriers and Improving the Skill with Model Errors for State Estimation and Prediction.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 13, 2019
- Source ID
- N000141912286
Entities
People
- Andrew Majda
Organizations
- New York University
- Office of Naval Research
- United States Navy