Enforcing Continuous Physical Symmetries in Deep Learning Network for
Solving Partial Differential Equations
- URL: http://arxiv.org/abs/2206.09299v1
- Date: Sun, 19 Jun 2022 00:44:22 GMT
- Title: Enforcing Continuous Physical Symmetries in Deep Learning Network for
Solving Partial Differential Equations
- Authors: Zhi-Yong Zhang, Hui Zhang, Li-Sheng Zhang, Lei-Lei Guo
- Abstract summary: We introduce a new method, symmetry-enhanced physics informed neural network (SPINN) where the invariant surface conditions induced by the Lie symmetries of PDEs are embedded into the loss function of PINN.
We show that SPINN performs better than PINN with fewer training points and simpler architecture of neural network.
- Score: 3.6317085868198467
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: As a typical {application} of deep learning, physics-informed neural network
(PINN) {has been} successfully used to find numerical solutions of partial
differential equations (PDEs), but how to improve the limited accuracy is still
a great challenge for PINN. In this work, we introduce a new method,
symmetry-enhanced physics informed neural network (SPINN) where the invariant
surface conditions induced by the Lie symmetries of PDEs are embedded into the
loss function of PINN, for improving the accuracy of PINN. We test the
effectiveness of SPINN via two groups of ten independent numerical experiments
for the heat equation, Korteweg-de Vries (KdV) equation and potential Burgers
{equations} respectively, which shows that SPINN performs better than PINN with
fewer training points and simpler architecture of neural network. Furthermore,
we discuss the computational overhead of SPINN in terms of the relative
computational cost to PINN and show that the training time of SPINN has no
obvious increases, even less than PINN for some cases.
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