Neural-network-based solvers for partial differential equations (PDEs) suffer from difficulties tackling high-frequency modes when learning complex functions, whereas for classical solvers it is more difficult to handle low-frequency modes. Zhang and colleagues propose a hybrid numerical PDE solver by combining a Deep Operator Network with traditional relaxation methods, leading to balanced convergence across the eigenmode spectrum for a wide range of PDEs.
- Enrui Zhang
- Adar Kahana
- George Em Karniadakis
