Abstract:Building upon the traditional PINN(physics-informed neural network), two improved methods for solving partial differential equations, EmPINN(expanding physics-informed neural network with modified multi-layer perceptron) and DL-PINN(diverse loss function physics-informed neural network), were presented by incorporating dimension expansion and diverse physics loss functions. EmPINN innovatively introduced a neural network structure with residual connections and a dimension-expanding mechanism. DL-PINN, based on EmPINN, combined the dimension-expanding mechanism with gradient enhancement and variational physical information to incorporate multiple physical information more effectively and improved the fitting capability of the neural network. Experimental results demonstrate that the proposed methods outperform traditional PINN method, improve solution accuracy by up to two orders of magnitude on different partial differential equation cases.