  There has been rapid progress recently on the application of deep networks to
the solution of partial differential equations, collectively labelled as
Physics Informed Neural Networks (PINNs). In this paper, we develop Physics
Informed Extreme Learning Machine (PIELM), a rapid version of PINNs which can
be applied to stationary and time dependent linear partial differential
equations. We demonstrate that PIELM matches or exceeds the accuracy of PINNs
on a range of problems. We also discuss the limitations of neural network based
approaches, including our PIELM, in the solution of PDEs on large domains and
suggest an extension, a distributed version of our algorithm -{}- DPIELM. We
show that DPIELM produces excellent results comparable to conventional
numerical techniques in the solution of time-dependent problems. Collectively,
this work contributes towards making the use of neural networks in the solution
of partial differential equations in complex domains as a competitive
alternative to conventional discretization techniques.
