GCN-FFNN: A two-stream deep model for learning solution to partial differential equations

This paper introduces a novel two-stream deep model based on graph convolutional network (GCN) architecture and feed-forward neural networks (FFNN) for learning the solution of nonlinear partial differential equations (PDEs). The aims at incorporating both grid input representations using two streams corresponding to GCN FFNN models, respectively. Each stream layer receives processes its representation. As opposed which grid-like structure, operates data where neighborhood information is incorporated through adjacency matrix graph. In this way, proposed GCN-FFNN learns from types representations, i.e. data, obtained via discretization PDE domain. trained in phases. first phase, parameters each are separately. Both employ same error function adjust their by enforcing models satisfy given as well initial boundary conditions or collocation (training) data. second learned layers frozen representation solutions fed fully connected whose previously used function. tested test located inside outside numerical results demonstrate applicability efficiency over individual 1D-Burgers, 1D-Schrödinger, 2D-Burgers, 2D-Schrödinger equations.