Towards General Neural Surrogate Solvers with Specialized Neural Accelerators

TL;DR

This paper introduces SNAP-DDM, a domain decomposition method leveraging specialized neural operators to accurately solve PDEs with arbitrary boundary conditions and geometries, enabling accelerated simulations in electromagnetics and fluid dynamics.

Contribution

It presents a novel neural surrogate solver framework that adapts to diverse PDE problems with variable geometries and boundary conditions, improving flexibility and accuracy.

Findings

Achieved near-unity accuracy with specialized neural operators.

Successfully applied to 2D electromagnetics and fluid flow problems.

Enabled accurate PDE solutions across a wide range of domain sizes.

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 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.