Sparse Representations of Complex Fluid Flows Over Spatially Global and Local Subspaces Through Machine Learning

Rohit Deshmukh, The Ohio State University
Lecture

Reduced Order Models for complex, dynamical systems are long sought to enable design, uncertainty quantification, control, and analysis. Conventional modal decomposition techniques, which often serve as a foundation for model reduction, are limited for multi-scale problems. Two new approaches, borrowing from machine learning and computational mechanics, are developed to exploit sparsity in dynamical systems. The first is based on sparse coding, which identifies a compact set of multi-scale modes that span a broad spectrum of system features. Such modes better balance production and dissipation of energy in the developed models. However, they also become inefficient at representing ultra-high dimensional systems. A potential solution to this latter problem is to exploit spatial sparsity through a Generalized Finite Element approach. This approach enables the linking of relatively simple, localized sub-spaces throughout a larger, highly complex domain. Current and potential data compression, rapid analysis, and predictive modeling applications are discussed.

Miscellaneous Information: 

This seminar will be streamed, see details at https://anlpress.cels.anl.gov/mcs-streaming-seminars