mlsanityData to 7 Oct 2026

CD-ROM: Complemented Deep-Reduced Order Model

arXiv 2202.10746 ↗First posted 22 Feb 2022physics.flu-dyn cs.LG stat.MLcited by 8

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 25 of its 77 references that are in the map. First posted on arXiv 22 Feb 2022.

Builds on

25 of 77 references.

References · 25

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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 2; 2024: 3; 2025: 2; 2026: 1.

8 papers.

  1. 2023Mori-Zwanzig latent space Koopman closure for nonlinear autoencodercited by 12
  2. 2023Interpretable learning of effective dynamics for multiscale systemscited by 11
  3. 2024NeurIPS 2024 ML4CFD Competition: Harnessing Machine Learning for Computational Fluid Dynamics in Airfoil Designcited by 8
  4. 2024ML4PhySim : Machine Learning for Physical Simulations Challenge (The airfoil design)cited by 3
  5. 2024Neural delay differential equations: learning non-Markovian closures for partially known dynamical systemscited by 1
  6. 2025UP-dROM : Uncertainty-Aware and Parametrised dynamic Reduced-Order Model, application to unsteady flowscited by 0
  7. 2025NeurIPS 2024 ML4CFD Competition: Results and Retrospective Analysiscited by 0
  8. 2026Efficient Adaptation of ROMs for Unsteady Flows Using Data Assimilationcited by 0