Towards General Neural Surrogate Solvers with Specialized Neural Accelerators

arXiv:2405.02351v1 Announce Type: new
Abstract: 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 …

abstract accelerator accelerators arxiv cs.ai cs.dc cs.lg differential differential equation domain equation general network neural network physics.optics snap solve systems type