  Physics Informed Neural Networks (PINNs) have recently gained popularity for
solving partial differential equations, given the fact they escape the curse of
dimensionality. In this paper, we present Physics Informed Neural Networks as
an underdetermined point matching collocation method then expose the connection
between Galerkin Least Square (GALS) and PINNs, to develop an a priori error
estimate, in the context of elliptic problems. In particular, techniques that
belong to the realm of least square finite elements and Rademacher complexity
analysis are used to obtain the error estimate.

Numerical Analysis;Numerical Analysis