  The use of deep learning methods for solving PDEs is a field in full
expansion. In particular, Physical Informed Neural Networks, that implement a
sampling of the physical domain and use a loss function that penalizes the
violation of the partial differential equation, have shown their great
potential. Yet, to address large scale problems encountered in real
applications and compete with existing numerical methods for PDEs, it is
important to design parallel algorithms with good scalability properties. In
the vein of traditional domain decomposition methods (DDM), we consider the
recently proposed deep-ddm approach. We present an extension of this method
that relies on the use of a coarse space correction, similarly to what is done
in traditional DDM solvers. Our investigations shows that the coarse correction
is able to alleviate the deterioration of the convergence of the solver when
the number of subdomains is increased thanks to an instantaneous information
exchange between subdomains at each iteration. Experimental results demonstrate
that our approach induces a remarkable acceleration of the original deep-ddm
method, at a reduced additional computational cost.
