论文标题
用于数据驱动的矢量 - 螺旋溶液和耦合非线性方程的参数发现的RAR-PINN算法
RAR-PINN algorithm for the data-driven vector-soliton solutions and parameter discovery of coupled nonlinear equations
论文作者
论文摘要
这项工作旨在提供一个有效的深度学习框架，以预测耦合非线性方程及其相互作用的矢量 - 索尔顿解决方案。我们在这里提出的方法是一种物理信息的神经网络（PINN），结合了基于残留的自适应改进（RAR-PINN）算法。与传统的PINN算法不同，该算法随机采用点，RAR-PINN算法使用一种自适应点提取方法来提高具有陡峭梯度的解决方案的训练效率。 RAR-PINN和传统PINN算法之间的一系列实验比较被实施到耦合的广义非线性Schrödinger（CGNLS）方程为例。结果表明，RAR-PINN算法具有更快的收敛速率和更好的近似能力，尤其是在对耦合系统中变化变形的矢量 - 索属相互作用进行建模时。最后，将RAR-PINN方法应用于执行CGNLS方程的数据驱动发现，该发现显示分散和非线性系数可以很好地近似。
This work aims to provide an effective deep learning framework to predict the vector-soliton solutions of the coupled nonlinear equations and their interactions. The method we propose here is a physics-informed neural network (PINN) combining with the residual-based adaptive refinement (RAR-PINN) algorithm. Different from the traditional PINN algorithm which takes points randomly, the RAR-PINN algorithm uses an adaptive point-fetching approach to improve the training efficiency for the solutions with steep gradients. A series of experiment comparisons between the RAR-PINN and traditional PINN algorithms are implemented to a coupled generalized nonlinear Schrödinger (CGNLS) equation as an example. The results indicate that the RAR-PINN algorithm has faster convergence rate and better approximation ability, especially in modeling the shape-changing vector-soliton interactions in the coupled systems. Finally, the RAR-PINN method is applied to perform the data-driven discovery of the CGNLS equation, which shows the dispersion and nonlinear coefficients can be well approximated.
