Densely Multiplied Physics Informed Neural Networks
- URL: http://arxiv.org/abs/2402.04390v2
- Date: Mon, 12 Feb 2024 20:40:44 GMT
- Title: Densely Multiplied Physics Informed Neural Networks
- Authors: Feilong Jiang, Xiaonan Hou, Min Xia
- Abstract summary: physics-informed neural networks (PINNs) have shown great potential in dealing with nonlinear partial differential equations (PDEs)
This paper improves the neural network architecture to improve the performance of PINN.
We propose a densely multiply PINN (DM-PINN) architecture, which multiplies the output of a hidden layer with the outputs of all the behind hidden layers.
- Score: 2.0853213407621
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Although physics-informed neural networks (PINNs) have shown great potential
in dealing with nonlinear partial differential equations (PDEs), it is common
that PINNs will suffer from the problem of insufficient precision or obtaining
incorrect outcomes. Unlike most of the existing solutions trying to enhance the
ability of PINN by optimizing the training process, this paper improved the
neural network architecture to improve the performance of PINN. We propose a
densely multiply PINN (DM-PINN) architecture, which multiplies the output of a
hidden layer with the outputs of all the behind hidden layers. Without
introducing more trainable parameters, this effective mechanism can
significantly improve the accuracy of PINNs. The proposed architecture is
evaluated on four benchmark examples (Allan-Cahn equation, Helmholtz equation,
Burgers equation and 1D convection equation). Comparisons between the proposed
architecture and different PINN structures demonstrate the superior performance
of the DM-PINN in both accuracy and efficiency.
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