Distentangling Turbulent Structure with Nonlinear Dynamics and Machine Learning
Abstract
The overall objective of the work performed under this grant was to integrate the dynamical systems approach to turbulent flows with ideas and tools from machine learning to develop and apply new approaches for the data-driven modeling and control of complex chaotic flow phenomena. Building on the observation above that very complex high-dimensional dynamics often lie on a surface (manifold) of much lower dimension, a central theme of the work is nonlinear dimension reduction, using machine learning to identify the manifold on which the data lie as well as the dynamical equations for the time-evolution of the system dynamics. Related to the issue of dimension reduction is that of modal decomposition of data -- for example, the classical proper orthogonal decomposition (POD) of flow data generates a set of basis vectors, and a reduced-dimensional representation of the data can be obtained by projection onto a subset of these vectors. (This is a linear dimension reduction process, which always projects data onto a flat surface. Nonlinear approaches like those that we use enable projection onto a curved manifold, and are thus often much more effective at dimension reduction than POD.) A number of specific accomplishments have been achieved. We have developed a new framework, which we call ``Data-driven Manifold Dynamics" (DManD), that enables development of high-fidelity low-dimensional dynamic models for complex chaotic processes.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 25, 2022
- Accession Number
- AD1230445
Entities
People
- Michael D. Graham
Organizations
- University of Wisconsin System