부산대학교 도서관

This paper focuses on the emerging branch of the deep learning technique that is employed in the various simple and nonlinear mathematical models of one and two-dimension. This numerical technique takes advantage of the backpropagation algorithm and computational graph of deep learning. A computational ability of a feedforward neural network (FNN) has been further employed, which utilized the randomly or uniformly sampled collocation points over the physical domain and different boundary conditions. Furthermore, a loss function is formulated based on the mathematical model and boundary conditions which is further enforced to minimize the unlabeled sampled points. The minimization process of the loss function is achieved through the various optimizer during the backpropagation algorithm. Eventually, the training process of FNN completes after getting an admissible error for the solution. Multiple examples are tested and cross-validated with the exact solutions for the problem. Furthermore, the DL-based solutions have a good agreement with the solution obtained from finite element approach, indicating that the DL-based numerical techniques can be considered an alternate numerical technique for solving various mathematical models.