Jan Rottmayer, TU Kaiserslautern
Title: Reduced Order Modeling and Nonlinear System Identification Techniques for Fluid Dynamics
Data-driven mathematical methods are increasingly important for characterizing complex dynamical systems across the physical and engineering domain. These methods discover and exploit a relatively small subset of the full high dimensional state space where low dimensional models can be used to capture the dominant system characteristics for control and prediction purposes. Even though data-driven methods are often sensitive to noise and require substantial amounts of data, with recent methods immense progress was made in developing robust methods in a low-data limit.
Emerging dimensionality reduction techniques offer to discover low-rank spatio-temporal patterns in the dynamics of the system, provide approximations in terms of linear dynamical systems and construct reduced order models in low dimensional embeddings. The reduction in computation offered by reduced order models facilitates the implementation in on-line model predicitve control providing a computationally efficient and robust control scheme.
In this talk we will take a look on recent advances in data-driven system identification and reduced order modelling, focusing on the work of Brunton et al., who proposed Dynamic Mode Decompositon with Control (DMDc) and Sparse Identification of Nonlinear Dynamics in Model Predictive Control (SINDy-MPC), and is a leading researcher on the field data-driven science and engineering.
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