Physics-informed deep learning for incompressible laminar flows
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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.
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- 2024DiffGrad for Physics-Informed Neural Networks5 Sep 2024
- 2024Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured grids15 Jun 2024
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- 2024VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior10 Jun 2024
- 2024Initialization-enhanced Physics-Informed Neural Network with Domain Decomposition (IDPINN)5 Jun 2024
- 2024A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains21 May 2024
- 2024The Principle of Minimum Pressure Gradient: An Alternative Basis for Physics-Informed Learning of Incompressible Fluid Mechanics15 Jan 2024
- 2023Theory and implementation of inelastic Constitutive Artificial Neural Networks10 Nov 2023
- 2023Filtered Partial Differential Equations: a robust surrogate constraint in physics-informed deep learning framework7 Nov 2023
- 2023Let Quantum Neural Networks Choose Their Own Frequencies6 Sep 2023
- 2023Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networks24 Aug 2023
- 2023Physics-informed neural network for seismic wave inversion in layered semi-infinite domain9 May 2023
- 2023Simulation and Prediction of Countercurrent Spontaneous Imbibition at Early and Late Times Using Physics-Informed Neural Networks6 May 2023
- 2023An Implicit GNN Solver for Poisson-like problems6 Feb 2023
- 2022FastFlow: AI for Fast Urban Wind Velocity Prediction22 Nov 2022
- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications15 Nov 2022
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- 2022Partial Differential Equations Meet Deep Neural Networks: A Survey27 Oct 2022
- 2022SeismicNet: Physics-informed neural networks for seismic wave modeling in semi-infinite domain25 Oct 2022
- 2022Robust Regression with Highly Corrupted Data via Physics Informed Neural Networks19 Oct 2022
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- 2022Transfer Learning as a Method to Reproduce High-Fidelity NLTE Opacities in Simulations28 May 2022
- 2022DropTrack -- automatic droplet tracking using deep learning for microfluidic applications5 May 2022
- 2022Investigation of Physics-Informed Deep Learning for the Prediction of Parametric, Three-Dimensional Flow Based on Boundary Data17 Mar 2022
- 2022Physics-informed neural network solution of thermo-hydro-mechanical (THM) processes in porous media3 Mar 2022
- 2022Physics-informed neural networks for non-Newtonian fluid thermo-mechanical problems: an application to rubber calendering process31 Jan 2022
- 2022Physics-informed neural networks for modeling rate- and temperature-dependent plasticity20 Jan 2022
- 2021Surrogate Model for Shallow Water Equations Solvers with Deep Learning20 Dec 2021
- 2021Stacked Generative Machine Learning Models for Fast Approximations of Steady-State Navier-Stokes Equations13 Dec 2021
- 2021A coarse space acceleration of deep-DDM7 Dec 2021
- 2021Physics informed neural networks for continuum micromechanics14 Oct 2021
- 2021Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training6 Oct 2021
- 2021SPATE-GAN: Improved Generative Modeling of Dynamic Spatio-Temporal Patterns with an Autoregressive Embedding Loss30 Sep 2021
- 2021PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs26 Jun 2021
- 2021Encoding physics to learn reaction-diffusion processes9 Jun 2021
- 2021BubbleNet: Inferring micro-bubble dynamics with semi-physics-informed deep learning15 May 2021
50 newest of 54 All 54 (JSON)
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- 2022Physics-Informed Machine Learning: A Survey on Problems, Methods and Applicationscited by 90
- 2022Mitigating Propagation Failures in Physics-informed Neural Networks using Retain-Resample-Release (R3) Samplingcited by 72
- 2022Neural Conservation Laws: A Divergence-Free Perspectivecited by 69
- 2021Encoding physics to learn reaction-diffusion processescited by 61
- 2021Physics informed neural networks for continuum micromechanicscited by 46
- 2021One-shot learning for solution operators of partial differential equationscited by 28
- 2021Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential trainingcited by 26
- 2022Partial Differential Equations Meet Deep Neural Networks: A Surveycited by 25
- 2022Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computingcited by 24
- 2023Let Quantum Neural Networks Choose Their Own Frequenciescited by 22
- 2023Solving Forward and Inverse Problems of Contact Mechanics using Physics-Informed Neural Networkscited by 17
12 most cited of 54 All 54 (JSON)
- 2026A Geometry-Aware Triplane Field Network for Vehicle Aerodynamic Prediction5 Jun 2026
- 2026Physics-Informed Transformer for Multi-Band Channel Frequency Response Reconstruction2 Apr 2026
- 2026Distributed physics-informed neural networks via domain decomposition for fast flow reconstruction5 Feb 2026
- 2025PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems29 Jul 2025
- 2025Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations17 Jul 2025
- 2025Resolving Extreme Data Scarcity by Explicit Physics Integration: An Application to Groundwater Heat Transport8 Jul 2025
- 2025Information-Theoretic Framework for Understanding Modern Machine-Learning9 Jun 2025
- 2025A Physics-Informed Spatiotemporal Deep Learning Framework for Turbulent Systems16 May 2025
- 2025Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning25 Apr 2025
- 2025DGenNO: A Novel Physics-aware Neural Operator for Solving Forward and Inverse PDE Problems based on Deep, Generative Probabilistic Modeling10 Feb 2025
- 2024DiffGrad for Physics-Informed Neural Networks5 Sep 2024
- 2024Finite-difference-informed graph network for solving steady-state incompressible flows on block-structured grids15 Jun 2024
12 newest of 54 All 54 (JSON)