Towards General Neural Surrogate Solvers with Specialized Neural Accelerators
This addresses the problem of inflexibility in neural PDE solvers for researchers in computational physics, though it is incremental as it builds on existing domain decomposition methods.
The paper tackled the limitation of neural PDE solvers to fixed domains by proposing SNAP-DDM, which uses specialized neural operators for subdomains to handle arbitrary conditions, achieving near unity accuracy in 2D electromagnetics and fluid flow problems.
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.