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Real-time simulation of parameter-dependent fluid flows through deep learning-based reduced order models

arXiv 2106.05722 ↗First posted 10 Jun 2021physics.flu-dyn cs.CE cs.LGcited by 12

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Abstract (arXiv)

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov-Galerkin projections) if a mixed velocity-pressure formulation is considered, possibly hampering the evaluation of reliable solutions in real-time. Dealing with fluid-structure interactions entails even higher difficulties. The proposed deep learning (DL)-based ROMs overcome all these limitations by learning in a non-intrusive way both the nonlinear trial manifold and the reduced dynamics. To do so, they rely on deep neural networks, after performing a former dimensionality reduction through POD enhancing their training times substantially. The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid-structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm.

Key facts. Cited by 12 papers in the map (data through 14 Oct 2026). Builds on 13 of its 77 references that are in the map. First posted on arXiv 10 Jun 2021.

Builds on

13 of 77 references.

References · 13

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1 more
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Citing papers per year: 2022: 6; 2023: 2; 2024: 2; 2025: 2.

12 papers.

  1. 2022Deep Learning Methods for Partial Differential Equations and Related Parameter Identification Problemscited by 34
  2. 2022Reduced order modeling of parametrized systems through autoencoders and SINDy approach: continuation of periodic solutionscited by 29
  3. 2022Multi-fidelity surrogate modeling using long short-term memory networkscited by 18
  4. 2023Multi-fidelity reduced-order surrogate modelingcited by 18
  5. 2022Long-time prediction of nonlinear parametrized dynamical systems by deep learning-based reduced order modelscited by 10
  6. 2023Multi-fidelity prediction of fluid flow and temperature field based on transfer learning using Fourier Neural Operatorcited by 10
  7. 2022CD-ROM: Complemented Deep-Reduced Order Modelcited by 8
  8. 2024Multi-fidelity physics constrained neural networks for dynamical systemscited by 5
  9. 2024PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEscited by 4
  10. 2025Improving Long-term Autoregressive Spatiotemporal Predictions: A Proof of Concept with Fluid Dynamicscited by 4
  11. 2022Virtual twins of nonlinear vibrating multiphysics microstructures: physics-based versus deep learning-based approachescited by 1
  12. 2025Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Modelscited by 1