Reduced-order Model for Fluid Flows via Neural Ordinary Differential Equations

Carlos José Gonzalez Rojas, Andreas Dengel, Mateus Dias Ribeiro

In: Combining Artificial Intelligence and Machine Learning with Physics Sciences. AAAI Spring Symposium (AAAI SSS-2021) March 22-24 Palo Alto California United States AAAI 2021.


Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can decrease the computational burden of numerical solutions, while preserving the most important features of complex physical problems. In this paper, we use the proper orthogonal decomposition to reduce the dimensionality of the model and introduce a novel generative neural ODE (NODE) architecture to forecast the behavior of the temporal coefficients. With this methodology, we replace the classical Galerkin projection with an architecture characterized by the use of a continuous latent space. We exemplify the methodology on the dynamics of the Von Karman vortex street of the flow past a cylinder generated by a Large-eddy Simulation (LES)-based code. We compare the NODE methodology with an LSTM baseline to assess the extrapolation capabilities of the generative model and present some qualitative evaluations of the flow reconstructions.

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2102.02248.pdf (pdf, 4 MB )

Deutsches Forschungszentrum für Künstliche Intelligenz
German Research Center for Artificial Intelligence