Speaker
Description
Data-driven modeling represents a fundamental technique in the analysis and design of complex dynamical systems. However, the direct application of machine learning algorithms is not an appropriate methodology for high-dimensional systems. A common approach to address this challenge is to utilize dimension reduction techniques, which inherently introduce additional errors in surrogate systems. Recently, some studies have focused on learning high-dimensional systems by exploiting the geometric structure of the underlying dynamics via the method of sparse Full-Order Model (sFOM) inference [1, 2, 3]. In this talk, we further investigate the sFOM inference in the context of incompressible fluid dynamics. We exploit the physics-based quadratic structure of the Navier-Stokes equations, as well as a sparse approximation for the system operators, dictated by geometrical adjacency. Using training data for the system states, we then solve “local", regularized least-squares problems for each system degree of freedom. This renders the data-driven inference and storage of the full-order operators feasible. We thus investigate the properties of the learned, sparse models for two incompressible fluid dynamics test-cases, namely the flow over a cylinder and the lid-driven cavity. We also examine the predictions of reduced-order models, derived from the inferred sFOM, via projection to a low-dimensional manifold through the Proper Orthogonal Decomposition (sFOM-POD). We highlight the potential change in stability and predictive capabilities of the learned dynamical systems.
References
[1] Y. Schumann and P. Neumann. On linear models for discrete operator inference in time dependent problems. Journal of Computational and Applied Mathematics, 425:115022, 2023.
[2] L. Gkimisis, T. Richter, and P. Benner. Adjacency-based, non-intrusive model reduction for vortex-induced vibrations. Computers \& Fluids 275 (2024): 106248.
[3] A. Prakash and Y. J. Zhang. Nonintrusive projection-based reduced order modeling using stable learned differential operators, arXiv preprint arXiv:2410.11253 (2024).
