Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating method

Understand

Physics-informed neural networks (PINNs) are appealing data-driven tools for solving and inferring solutions to nonlinear partial differential equations (PDEs).

• Unlike traditional neural networks (NNs), which train only on solution data, a PINN incorporates a PDE's residual into its loss function and trains to minimize the said residual at a set of collocation points in the solution domain.
• This paper explores the use of the Schwarz alternating method as a means to couple PINNs with each other and with conventional numerical models (i.e., full order models, or FOMs, obtained via the finite element, finite difference or finite volume methods) following a decomposition of the physical domain.
• It is well-known that training a PINN can be difficult when the PDE solution has steep gradients.