mlsanityData to 7 Oct 2026

Performance and accuracy assessments of an incompressible fluid solver coupled with a deep Convolutional Neural Network

arXiv 2109.09363 ↗First posted 20 Sep 2021physics.flu-dyn cs.LGcited by 8

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Abstract (arXiv)

The resolution of the Poisson equation is usually one of the most computationally intensive steps for incompressible fluid solvers. Lately, Deep Learning, and especially Convolutional Neural Networks (CNN), has been introduced to solve this equation, leading to significant inference time reduction at the cost of a lack of guarantee on the accuracy of the solution. This drawback might lead to inaccuracies and potentially unstable simulations. It also makes impossible a fair assessment of the CNN speedup, for instance, when changing the network architecture, since evaluated at different error levels. To circumvent this issue, a hybrid strategy is developed, which couples a CNN with a traditional iterative solver to ensure a user-defined accuracy level. The CNN hybrid method is tested on two flow cases, consisting of a variable-density plume with and without obstacles, demostrating remarkable generalization capabilities, ensuring both the accuracy and stability of the simulations. The error distribution of the predictions using several network architectures is further investigated. Results show that the threshold of the hybrid strategy defined as the mean divergence of the velocity field is ensuring a consistent physical behavior of the CNN-based hybrid computational strategy. This strategy allows a systematic evaluation of the CNN performance at the same accuracy level for various network architectures. In particular, the importance of incorporating multiple scales in the network architecture is demonstrated, since improving both the accuracy and the inference performance compared with feedforward CNN architectures, as these networks can provide solutions 1 10-25 faster than traditional iterative solvers.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 27 of its 104 references that are in the map. First posted on arXiv 20 Sep 2021.

Builds on

27 of 104 references.

References · 27

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15 more
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 1; 2023: 2; 2024: 3; 2025: 0; 2026: 1.

8 papers.

  1. 2024Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equationscited by 87
  2. 2021Using neural networks to solve the 2D Poisson equation for electric field computation in plasma fluid simulationscited by 10
  3. 2023Invariant preservation in machine learned PDE solvers via error correctioncited by 7
  4. 2023An Implicit GNN Solver for Poisson-like problemscited by 3
  5. 2022DS-GPS : A Deep Statistical Graph Poisson Solver (for faster CFD simulations)cited by 2
  6. 2024Multi-Level GNN Preconditioner for Solving Large Scale Problemscited by 0
  7. 2024Coupling Machine Learning Local Predictions with a Computational Fluid Dynamics Solver to Accelerate Transient Buoyant Plume Simulationscited by 0
  8. 2026Acceleration of an algebraic multigrid pressure solver using graph neural networkscited by 0