mlsanityData to 14 Oct 2026

Convolutional Autoencoders, Clustering and POD for Low-dimensional Parametrization of Navier-Stokes Equations

arXiv 2302.01278 ↗First posted 2 Feb 2023math.DS cs.LGcited by 3

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Abstract (arXiv)

Simulations of large-scale dynamical systems require expensive computations. Low-dimensional parametrization of high-dimensional states such as Proper Orthogonal Decomposition (POD) can be a solution to lessen the burdens by providing a certain compromise between accuracy and model complexity. However, for really low-dimensional parametrizations (for example for controller design) linear methods like the POD come to their natural limits so that nonlinear approaches will be the methods of choice. In this work we propose a convolutional autoencoder (CAE) consisting of a nonlinear encoder and an affine linear decoder and consider combinations with k-means clustering for improved encoding performance. The proposed set of methods is compared to the standard POD approach in two cylinder-wake scenarios modeled by the incompressible Navier-Stokes equations.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 15 of its 39 references that are in the map. First posted on arXiv 2 Feb 2023.

Builds on

15 of 39 references.

References · 15

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3 more
  1. 2021Robust output-feedback stabilization for incompressible flows using low-dimensional H∞-controllerscited by 3
  2. 2022Learning finite difference methods for reaction-diffusion type equations with FCNNcited by 3
  3. 2018Global Stabilization of Two Dimensional Viscous Burgers' Equation by Nonlinear Neumann Boundary Feedback Control and its Finite Element Analysiscited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 1.

3 papers.

  1. 2024Deep polytopic autoencoders for low-dimensional linear parameter-varying approximations and nonlinear feedback designcited by 0
  2. 2025Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical systemcited by 0
  3. 2026Generative prediction of laser-induced rocket ignition with dynamic latent space representationscited by 0