Adaptive Domain Decomposition for Finite Basis Physics-Informed Neural Networks

Sarah Helfert, Wanxin Chen, Amanda A. Howard, Panos Stinis, Alexander Heinlein

In this work, we present adaptive domain decomposition finite basis physics-informed neural networks (ADD-FBPINNs). The proposed method integrates Partition of Unity Networks (POUNets), a data-driven approach for learning domain partitions, with finite Basis physics-informed neural networks (FBPINNs) to perform more efficient domain decomposition and achieve more accurate approximations. FBPINNs improve upon the accuracy of standard physics-informed neural networks (PINNs) through user-defined subdivisions of the computational domain. By adapting the domain decomposition based on the solution's features using a separable POUNet, the framework can automatically learn partitions that are stable and can be geometrically interpretable. We test this approach on the two-dimensional Helmholtz equation, two-dimensional Poisson equation with multiscale features, and viscous Burgers equation and observe improved accuracy compared with FBPINNs with fixed domain decomposition.