  Surrogate neural network-based partial differential equation (PDE) solvers
have the potential to solve PDEs in an accelerated manner, but they are largely
limited to systems featuring fixed domain sizes, geometric layouts, and
boundary conditions. We propose Specialized Neural Accelerator-Powered Domain
Decomposition Methods (SNAP-DDM), a DDM-based approach to PDE solving in which
subdomain problems containing arbitrary boundary conditions and geometric
parameters are accurately solved using an ensemble of specialized neural
operators. We tailor SNAP-DDM to 2D electromagnetics and fluidic flow problems
and show how innovations in network architecture and loss function engineering
can produce specialized surrogate subdomain solvers with near unity accuracy.
We utilize these solvers with standard DDM algorithms to accurately solve
freeform electromagnetics and fluids problems featuring a wide range of domain
sizes.
