NSFnets
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.
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References in zbMATH (referenced in 26 articles , 1 standard article )
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Sorted by year (- Lou, Qin; Meng, Xuhui; Karniadakis, George Em: Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation (2021)
- Ranade, Rishikesh; Hill, Chris; Pathak, Jay: Discretizationnet: a machine-learning based solver for Navier-Stokes equations using finite volume discretization (2021)
- 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)
- Xiao, Tianbai; Frank, Martin: Using neural networks to accelerate the solution of the Boltzmann equation (2021)
- Jagtap, Ameya D.; Karniadakis, George Em: Extended physics-informed neural networks (XPINNs): a generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations (2020)
- Wang, Bo; Zhang, Wenzhong; Cai, Wei: Multi-scale deep neural network (MscaleDNN) methods for oscillatory Stokes flows in complex domains (2020)