CD-ROM: Complemented Deep- Reduced order model

Model order reduction through the POD-Galerkin method can lead to dramatic gains in terms of computational efficiency in solving physical problems. However, the applicability of the method to non linear high-dimensional dynamical systems such as the Navier-Stokes equations has been shown to be limited, producing inaccurate and sometimes unstable models. This paper proposes a deep learning based closure modeling approach for classical POD-Galerkin reduced order models (ROM). The proposed approach is theoretically grounded, using neural networks to approximate well studied operators. In contrast with most previous works, the present CD-ROM approach is based on an interpretable continuous memory formulation, derived from simple hypotheses on the behavior of partially observed dynamical systems. The final corrected models can hence be simulated using most classical time stepping schemes. The capabilities of the CD-ROM approach are demonstrated on two classical examples from Computational Fluid Dynamics, as well as a parametric case, the Kuramoto-Sivashinsky equation. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This paper proposes a deep learning based closure modeling approach for improving classical POD-Galerkin reduced order models (ROM), which uses neural networks to approximate well studied operators. The approach is based on an interpretable continuous memory formulation, resulting in corrected models that can be simulated using classical time stepping schemes. The capabilities of the approach are demonstrated on two classical examples from Computational Fluid Dynamics and a parametric case.