A Neural Network-based Pde Solving Algorithm With High Precision

This article introduces a new method for solving large-scale linear equations based on deep neural networks. The residual network architecture and the correction iteration inspired by classic iteration methods are employed to achieve a high accuracy. Numerical results show that this DNN-based technique is capable of obtaining an error of less than 10-7 and its computation time is less sensitive to the problem size than that of classic iterative methods.