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.

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