NSFnets
swMATH ID:  42059 
Software Authors:  Xiaowei Jin, Shengze Cai, Hui Li, George Em Karniadakis 
Description:  NSFnets (NavierStokes Flow nets): Physicsinformed neural networks for the incompressible NavierStokes equations. We employ physicsinformed 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 NavierStokes equations: the velocitypressure (VP) formulation and the vorticityvelocity (VV) formulation. We refer to these specific PINNs for the NavierStokes 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 VPNSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VVNSFnet. These two different forms of the NavierStokes 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 VPNSFnet, 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. 
Homepage:  https://arxiv.org/abs/2003.06496 
Related Software:  Adam; DeepXDE; DiffSharp; TensorFlow; DGM; DeepONet; PINNsNTK; XPINNs; FPINNs; GitHub; PyTorch; LBFGS; DiscretizationNet; SciANN; VarNet; SimNet; PDENet; D3M; PINNeik; NeuralPDE.jl 
Referenced in:  27 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

NSFnets (NavierStokes flow nets): physicsinformed neural networks for the incompressible NavierStokes equations. Zbl 07510065 Jin, Xiaowei; Cai, Shengze; Li, Hui; Karniadakis, George Em 
2021

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Referenced by 80 Authors
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Referenced in 7 Serials
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