A Multi-layer Composite Radial Basis Neural Network Combined with PINN to Solve Partial Differential Equations

A novel approach for solving partial differential equations (PDEs) is introduced in this paper by integrating a multi-layer composite radial basis neural network (MCRBNN) with a physical information neural network (PINN). Initially, a multi-layer radial basis function neural network (RBFNN) is constructed, and the optimal number of structural layers is determined. Subsequently, sub-networks are integrated into each layer to form a composite multi-layer RBFNN. Adjustable radial basis functions are used in each layer of subnetworks. To address the sensitivity of RBFNN to initial parameter values, particularly the center and width of the radial basis function, the last layer is augmented with a PINN. The performance and effectiveness of the method in PDEs are demonstrated through two numerical experiments. Moreover, its outstanding solution accuracy and speed are highlighted, even when the quantity of training samples remains unchanged in comparison with those of some existing methods.