mlsanityData to 13 Oct 2026

Physics-informed deep learning for incompressible laminar flows

arXiv 2002.10558 ↗First posted 24 Feb 2020physics.flu-dyn cs.LG physics.comp-phcited by 54

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Abstract (arXiv)

Physics-informed deep learning has drawn tremendous interest in recent years to solve computational physics problems, whose basic concept is to embed physical laws to constrain/inform neural networks, with the need of less data for training a reliable model. This can be achieved by incorporating the residual of physics equations into the loss function. Through minimizing the loss function, the network could approximate the solution. In this paper, we propose a mixed-variable scheme of physics-informed neural network (PINN) for fluid dynamics and apply it to simulate steady and transient laminar flows at low Reynolds numbers. A parametric study indicates that the mixed-variable scheme can improve the PINN trainability and the solution accuracy. The predicted velocity and pressure fields by the proposed PINN approach are also compared with the reference numerical solutions. Simulation results demonstrate great potential of the proposed PINN for fluid flow simulation with a high accuracy.

Key facts. Cited by 54 papers in the map (data through 13 Oct 2026). First posted on arXiv 24 Feb 2020.

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Citing papers per year: 2021: 13; 2022: 18; 2023: 7; 2024: 6; 2025: 7; 2026: 3.

54 papers.

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  1. 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEscited by 98
  2. 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 90
  3. 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 72
  4. 2022Neural Conservation Laws: A Divergence-Free Perspectivecited by 69
  5. 2021Encoding physics to learn reaction-diffusion processescited by 61
  6. 2021Physics informed neural networks for continuum micromechanicscited by 46
  7. 2021One-shot learning for solution operators of partial differential equationscited by 28
  8. 2021Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential trainingcited by 26
  9. 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
  10. 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
  11. 2023Let Quantum Neural Networks Choose Their Own Frequenciescited by 22
  12. 2023Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networkscited by 17
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  1. 2022SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domaincited by 16
  2. 2024A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domainscited by 15
  3. 2021SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Losscited by 13
  4. 2024VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behaviorcited by 13
  5. 2023Theory and implementation of inelastic Constitutive Artificial Neural Networkscited by 12
  6. 2022Physics-informed neural networks for modeling rate- and temperature-dependent plasticitycited by 11
  7. 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)cited by 9
  8. 2021Hard Encoding of Physics for Learning Spatiotemporal Dynamicscited by 8
  9. 2021A coarse space acceleration of deep-DDMcited by 8
  10. 2022Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous mediacited by 8
  11. 2022A composable machine-learning approach for steady-state simulations on high-resolution gridscited by 8
  12. 2022PhySRNet: Physics informed super-resolution network for application in computational solid mechanicscited by 7
  13. 2022Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering processcited by 6
  14. 2022Inverse modeling of nonisothermal multiphase poromechanics using physics-informed neural networkscited by 6
  15. 2022PhyGNNet: Solving spatiotemporal PDEs with Physics-informed Graph Neural Networkcited by 5
  16. 2025DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modelingcited by 5
  17. 2021A Latent space solver for PDE generalizationcited by 4
  18. 2021BubbleNet: Inferring micro-bubble dynamics with semi-physics-informed deep learningcited by 4
  19. 2022Robust Regression with Highly Corrupted Data via Physics Informed Neural Networkscited by 4
  20. 2023An Implicit GNN Solver for Poisson-like problemscited by 3
  21. 2021Geometry encoding for numerical simulationscited by 2
  22. 2021Surrogate Model for Shallow Water Equations Solvers with Deep Learningcited by 2
  23. 2022Investigation of Physics-Informed Deep Learning for the Prediction of Parametric, Three-Dimensional Flow Based on Boundary Datacited by 2
  24. 2022DropTrack -- automatic droplet tracking using deep learning for microfluidic applicationscited by 2
  25. 2023Physics-informed neural network for seismic wave inversion in layered semi-infinite domaincited by 2
  26. 2025Information-Theoretic Framework for Understanding Modern Machine-Learningcited by 2
  27. 2025PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problemscited by 2
  28. 2022Transfer Learning as a Method to Reproduce High-Fidelity NLTE Opacities in Simulationscited by 1
  29. 2022FastFlow: AI for Fast Urban Wind Velocity Predictioncited by 1
  30. 2023Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Times Using Physics-Informed Neural Networkscited by 1
  31. 2023Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning frameworkcited by 1
  32. 2024Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured gridscited by 1
  33. 2025Resolving Extreme Data Scarcity by Explicit Physics Integration: An Application to Groundwater Heat Transportcited by 1
  34. 2025Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equationscited by 1
  35. 2026Distributed physics-informed neural networks via domain decomposition for fast flow reconstructioncited by 1
  36. 2026Physics-Informed Transformer for Multi-Band Channel Frequency Response Reconstructioncited by 1
  37. 2026A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Predictioncited by 1
  38. 2021Stacked Generative Machine Learning Models for Fast Approximations of Steady-State Navier-Stokes Equationscited by 0

50 most cited of 54 All 54 (JSON)