NSFnets (Navier-Stokes Flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations. We employ physics-informed neural networks (PINNs) to simulate the incompressible flows ranging from laminar to turbulent flows. We perform PINN simulations by considering two different formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. We refer to these specific PINNs for the Navier-Stokes flow nets as NSFnets. Analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. These two different forms of the Navier-Stokes equations together with the initial and boundary conditions are embedded into the loss function of the PINNs. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without splitting the equations. We obtain good accuracy of the NSFnet simulation results upon convergence of the loss function, verifying that NSFnets can effectively simulate complex incompressible flows using either the VP or the VV formulations. We also perform a systematic study on the weights used in the loss function for the data/physics components and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. Our results suggest that the accuracy of NSFnets, for both laminar and turbulent flows, can be improved with proper tuning of weights (manual or dynamic) in the loss function.

References in zbMATH (referenced in 23 articles , 1 standard article )

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  1. Bai, Jinshuai; Zhou, Ying; Ma, Yuwei; Jeong, Hyogu; Zhan, Haifei; Rathnayaka, Charith; Sauret, Emilie; Gu, Yuantong: A general neural particle method for hydrodynamics modeling (2022)
  2. Bai, Xiao-Dong; Zhang, Wei: Machine learning for vortex induced vibration in turbulent flow (2022)
  3. Bihlo, Alex; Popovych, Roman O.: Physics-informed neural networks for the shallow-water equations on the sphere (2022)
  4. Chiu, Pao-Hsiung; Wong, Jian Cheng; Ooi, Chinchun; Dao, My Ha; Ong, Yew-Soon: CAN-PINN: a fast physics-informed neural network based on coupled-automatic-numerical differentiation method (2022)
  5. Gao, Han; Zahr, Matthew J.; Wang, Jian-Xun: Physics-informed graph neural Galerkin networks: a unified framework for solving PDE-governed forward and inverse problems (2022)
  6. Li, Liangliang; Li, Yunzhu; Du, Qiuwan; Liu, Tianyuan; Xie, Yonghui: ReF-nets: physics-informed neural network for Reynolds equation of gas bearing (2022)
  7. Lin, Shuning; Chen, Yong: A two-stage physics-informed neural network method based on conserved quantities and applications in localized wave solutions (2022)
  8. Liu, Yujie; Yang, Chao: VPVnet: a velocity-pressure-vorticity neural network method for the Stokes’ equations under reduced regularity (2022)
  9. Lucor, Didier; Agrawal, Atul; Sergent, Anne: Simple computational strategies for more effective physics-informed neural networks modeling of turbulent natural convection (2022)
  10. Psaros, Apostolos F.; Kawaguchi, Kenji; Karniadakis, George Em: Meta-learning PINN loss functions (2022)
  11. Ren, Pu; Rao, Chengping; Liu, Yang; Wang, Jian-Xun; Sun, Hao: PhyCRNet: physics-informed convolutional-recurrent network for solving spatiotemporal PDEs (2022)
  12. Wang, Hengjie; Planas, Robert; Chandramowlishwaran, Aparna; Bostanabad, Ramin: Mosaic flows: a transferable deep learning framework for solving PDEs on unseen domains (2022)
  13. Wang, Sifan; Yu, Xinling; Perdikaris, Paris: When and why PINNs fail to train: a neural tangent kernel perspective (2022)
  14. Cai, Shengze; Wang, Zhicheng; Lu, Lu; Zaki, Tamer A.; Karniadakis, George Em: DeepM&Mnet: inferring the electroconvection multiphysics fields based on operator approximation by neural networks (2021)
  15. Cao, Rushi; Cao, Ruyun: Computer simulation of water flow animation based on two-dimensional Navier-Stokes equations (2021)
  16. Gao, Han; Sun, Luning; Wang, Jian-Xun: PhyGeoNet: physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain (2021)
  17. Jin, Xiaowei; Cai, Shengze; Li, Hui; Karniadakis, George Em: NSFnets (Navier-Stokes flow nets): physics-informed neural networks for the incompressible Navier-Stokes equations (2021)
  18. Lou, Qin; Meng, Xuhui; Karniadakis, George Em: Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation (2021)
  19. Ranade, Rishikesh; Hill, Chris; Pathak, Jay: Discretizationnet: a machine-learning based solver for Navier-Stokes equations using finite volume discretization (2021)
  20. Wang, Sifan; Wang, Hanwen; Perdikaris, Paris: On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks (2021)

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