课程-迁移学习物理信息神经网络用于长时间非线性波传播模拟

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

由于传统物理信息神经网络(PINN)在长时间模拟时存在计算稳定性差甚至无法获得有效解的难题,文章提出了一种基于课程学习和迁移学习的物理信息神经网络(CTL-PINN),用于长时间非线性波传播模拟.该改进的PINN的主要思想是将原长时间历程问题转化成若干个短时间子问题,其求解过程分为3个阶段;在初始阶段,使用传统PINN来获得初始短期子问题的解;在课程学习阶段,使用包含前一步训练信息的传统PINN以时域扩大的方式逐次求解,在迁移学习阶段,使用包含前一步训练信息的传统PINN以时域迁移的方式逐次求解.这种改进的PINN可以避免传统PINN陷入局部最优解的问题.最后通过几个基准算例验证了本文所提出的CTL-PINN方法在模拟长时间非线性波传播过程的有效性和鲁棒性.

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.