mlsanityData to 7 Oct 2026

An artificial neural network approach to bifurcating phenomena in computational fluid dynamics

arXiv 2109.10765 ↗First posted 22 Sep 2021physics.flu-dyn cs.LG cs.NAcited by 11

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Abstract (arXiv)

This work deals with the investigation of bifurcating fluid phenomena using a reduced order modelling setting aided by artificial neural networks. We discuss the POD-NN approach dealing with non-smooth solutions set of nonlinear parametrized PDEs. Thus, we study the Navier-Stokes equations describing: (i) the Coanda effect in a channel, and (ii) the lid driven triangular cavity flow, in a physical/geometrical multi-parametrized setting, considering the effects of the domain's configuration on the position of the bifurcation points. Finally, we propose a reduced manifold-based bifurcation diagram for a non-intrusive recovery of the critical points evolution. Exploiting such detection tool, we are able to efficiently obtain information about the pattern flow behaviour, from symmetry breaking profiles to attaching/spreading vortices, even at high Reynolds numbers.

Key facts. Cited by 11 papers in the map (data through 7 Oct 2026). Builds on 7 of its 64 references that are in the map. First posted on arXiv 22 Sep 2021.

Builds on

7 of 64 references.

References · 7

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  2. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  3. 2020Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating PDEscited by 115
  4. 2020A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEscited by 105
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 2; 2024: 4; 2025: 3; 2026: 1.

11 papers.

  1. 2023A graph convolutional autoencoder approach to model order reduction for parametrized PDEscited by 44
  2. 2024GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applicationscited by 10
  3. 2024A practical existence theorem for reduced order models based on convolutional autoencoderscited by 9
  4. 2022Non-linear manifold ROM with Convolutional Autoencoders and Reduced Over-Collocation methodcited by 7
  5. 2024Neural networks for bifurcation and linear stability analysis of steady states in partial differential equationscited by 5
  6. 2024Neural empirical interpolation method for nonlinear model reductioncited by 4
  7. 2023Optimal Transport-inspired Deep Learning Framework for Slow-Decaying Kolmogorov n-width Problems: Exploiting Sinkhorn Loss and Wasserstein Kernelcited by 2
  8. 2025Time Extrapolation with Graph Convolutional Autoencoder and Tensor Train Decompositioncited by 2
  9. 2025Operator-based machine learning framework for generalizable prediction of unsteady treatment dynamics in stormwater infrastructurecited by 0
  10. 2025Adaptive Sampling for Hydrodynamic Stabilitycited by 0
  11. 2026Latent Dynamics Graph Convolutional Networks for model order reduction of parameterized time-dependent PDEscited by 0