  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 or non-classical symmetries of
PDEs are embedded into the loss function in PINN, to improve the accuracy of
PINN for solving the forward and inverse problems of PDEs. We test the
effectiveness of SPINN for the forward problem via two groups of ten
independent numerical experiments using different numbers of collocation points
and neurons for the heat equation, Korteweg-de Vries (KdV) equation and
potential Burgers {equations} respectively, and for the inverse problem by
considering different layers and neurons as well as different training points
for the Burgers equation in potential form. The numerical results show 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 certain cases.
