Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
MACHINE LEARNING-BASED REDUCED-ORDER MODELS FOR BURGERS AND SHALLOW-WATER EQUATIONS
Submission Author:
Pedro Roberto Barbosa Rocha , RJ
Co-Authors:
Pedro Roberto Barbosa Rocha, Marcos Sebastião de Paula Gomes
Presenter: Pedro Roberto Barbosa Rocha
doi://10.26678/ABCM.COBEM2023.COB2023-1592
Abstract
Scientific machine learning methods that incorporate physics knowledge on a data-driven learning have become quite promising for the representation and prediction of nonlinear fluid flow systems with multiple scales in space and time. This work addresses one of these methods, the Operator Inference (OpInf), in the context of model order reduction. By solving a multivariable regression problem in latent space, the OpInf seeks for optimal low-dimensional operators that represent the system dynamics. Its capabilities are illustrated throughout this paper and compared with popular machine learning frameworks found in literature, such as physics-informed neural networks (PINNs), Fourier neural operators (FNOs) and auto-encoding neural networks (U-Nets). Two representative cases with known physical parameters were evaluated: Burgers and shallow-water equations. The predictive performance of the reduced-order model (ROM) was assessed for each case and normalized root-mean-square errors were computed for the state variables of interest. For instance, they were below 6.2% for the dependent variable of the Burgers equation at the middle of the one-dimensional domain. Moreover, OpInf-based models require much less training time than neural networks since they have a small number of hyperparameters to be tuned. While here the ROM for the shallow-water equations took 25 seconds to be trained, it was recently reported in literature that more than 10 minutes were required to train a PINN-based surrogate model using the same training dataset. All these features highlight the great potential of the non-intrusive operator inference framework for model order reduction of fluid flow systems.
Keywords
Scientific Machine Learning, Model order reduction, fluid dynamics
