mlsanityData to 7 Oct 2026

Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation method

arXiv 2203.00360 ↗First posted 1 Mar 2022math.NA cs.LG cs.NAcited by 7

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Abstract (arXiv)

Non-affine parametric dependencies, nonlinearities and advection-dominated regimes of the model of interest can result in a slow Kolmogorov n-width decay, which precludes the realization of efficient reduced-order models based on linear subspace approximations. Among the possible solutions, there are purely data-driven methods that leverage autoencoders and their variants to learn a latent representation of the dynamical system, and then evolve it in time with another architecture. Despite their success in many applications where standard linear techniques fail, more has to be done to increase the interpretability of the results, especially outside the training range and not in regimes characterized by an abundance of data. Not to mention that none of the knowledge on the physics of the model is exploited during the predictive phase. In order to overcome these weaknesses, we implement the non-linear manifold method introduced by Carlberg et al [37] with hyper-reduction achieved through reduced over-collocation and teacher-student training of a reduced decoder. We test the methodology on a 2d non-linear conservation law and a 2d shallow water models, and compare the results obtained with a purely data-driven method for which the dynamics is evolved in time with a long-short term memory network.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 14 of its 57 references that are in the map. First posted on arXiv 1 Mar 2022.

Builds on

14 of 57 references.

References · 14

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2 more
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Cited by year

Citing papers per year: 2022: 3; 2023: 3; 2024: 1.

7 papers.

  1. 2022Neural Galerkin Schemes with Active Learning for High-Dimensional Evolution Equationscited by 55
  2. 2024A practical existence theorem for reduced order models based on convolutional autoencoderscited by 9
  3. 2023Generative Adversarial Reduced Order Modellingcited by 7
  4. 2022A Continuous Convolutional Trainable Filter for Modelling Unstructured Datacited by 5
  5. 2022Towards a machine learning pipeline in reduced order modelling for inverse problems: neural networks for boundary parametrization, dimensionality reduction and solution manifold approximationcited by 4
  6. 2023A two stages Deep Learning Architecture for Model Reduction of Parametric Time-Dependent Problemscited by 1
  7. 2023Hyper-Reduced Autoencoders for Efficient and Accurate Nonlinear Model Reductionscited by 0