Physically plausible and conservative solutions to Navier-Stokes equations using physics-informed CNNs
The physics-informed neural network(PINN)is an emerging approach for efficiently solving partial differen-tial equations(PDEs)using neural networks.The physics-informed convolutional neural network(PICNN),a variant of PINN enhanced by convolutional neural networks(CNNs),has achieved better results on a series of PDEs since the parameter-sharing property of CNNs is effective in learning spatial dependencies.However,applying existing PICNN-based methods to solve Navier-Stokes equations can generate oscillating predictions,which are inconsistent with the laws of physics and the conservation properties.To address this issue,we propose a novel method that combines PICNN with the finite volume method to obtain physically plausible and conservative solutions to Navier-Stokes equations.We derive the second-order upwind difference scheme of Navier-Stokes equations using the finite volume method.Then we use the derived scheme to calculate the partial derivatives and construct the physics-informed loss function.The proposed method is assessed by experiments on steady-state Navier-Stokes equations under different scenarios,including convective heat transfer and lid-driven cavity flow.The experimental results demonstrate that our method can effectively improve the plausibility and accuracy of the predicted solutions from PICNN.
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