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.

翻译：基于代理神经网络的偏微分方程求解器具有加速求解偏微分方程的潜力，但其应用在很大程度上受限于具有固定域尺寸、几何布局和边界条件的系统。我们提出了专用神经加速器驱动的域分解方法，这是一种基于域分解方法的偏微分方程求解方法，其中包含任意边界条件和几何参数的子域问题通过使用一组专用神经算子来精确求解。我们将该方法定制应用于二维电磁学和流体流动问题，并展示了网络架构和损失函数工程方面的创新如何能够产生具有近乎一致精度的专用代理子域求解器。我们利用这些求解器结合标准的域分解算法，精确求解了具有广泛域尺寸范围的无约束电磁学和流体问题。