CURRICULUM-TRANSFER-LEARNING BASED PHYSICS-INFORMED NEURAL NETWORKS FOR LONG-TIME SIMULATION OF NONLINEAR WAVE PROPAGATION

Due to the computational instability to obtain effective solutions in long-term evolution simulation by using the standard physics-informed neural networks (PINN), this paper develops a curriculum-transfer-learning based physics-informed neural networks (CTL-PINN) for long-term nonlinear wave propagation simulation. In the present CTL-PINN, the original long-term problem is transformed into several short-term sub-problems, and the solving process includes the following three stages. In the initial stage, we employ the standard PINN to obtain the solution of the initial short-term sub-problem, and then in the curriculum learning stage the standard PINN with the training information in the previous step is successively used to solve the problem with time domain extension, and next in the transfer learning stage the standard PINN with the training information in the previous step is successively used to solve the problem with time domain transfer. This improved PINN can avoid obtaining the local optimal solutions by using the standard PINN. Finally, several benchmark examples are used to verify the effectiveness and robustness of the proposed CTL-PINN in the solution of long-term nonlinear wave propagation problems.