  In recent years, physical informed neural networks (PINNs) have been shown to
be a powerful tool for solving PDEs empirically. However, numerical analysis of
PINNs is still missing. In this paper, we prove the convergence rate to PINNs
for the second order elliptic equations with Dirichlet boundary condition, by
establishing the upper bounds on the number of training samples, depth and
width of the deep neural networks to achieve desired accuracy. The error of
PINNs is decomposed into approximation error and statistical error, where the
approximation error is given in $C^2$ norm with $\mathrm{ReLU}^{3}$ networks
(deep network with activations function $\max\{0,x^3\}$) and the statistical
error is estimated by Rademacher complexity. We derive the bound on the
Rademacher complexity of the non-Lipschitz composition of gradient norm with
$\mathrm{ReLU}^{3}$ network, which is of immense independent interest.
