Rogue wave solutionGenuine rational soliton solutionsOne-rational soliton solutionThe solving of the derivative nonlinear Schrodinger equation (DNLS) has attracted considerable attention in theoretical analysis and physical applications. Based on the physics-informed neural network (PINN) which has been put...
Neural network method for solving analytical solution: (神经网络求解偏微分方程解析解的方法:) [1]R. F. Zhang, M. C. Li, M. Albishari, F. C. Zheng, Z. Z. Lan, "[Generalized lump solutions, classical lump solutions and rogue waves of the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera...
Layer_training_data_generation*.m: Matlab code for generating training and test data Citation information If you find our codes and publications helpful, please kindly cite the following publications. @article{song2020solving, title={Solving the frequency-domain acoustic VTI wave equation using physics...
For the first example, consider the following two-dimensional Helmholtz equation: (16)k2u+∂2u∂x2+∂2u∂y2=f,where k and f are the wave number and source term, respectively. We consider a square domain of length 2 units with the boundary condition, u=0 for the entire boundary....
Recently, researchers have explored the potential of physics-informed neural networks (PINNs) in solving the Helmholtz equation with limited success. While a number of attractive features have been demonstrated for the PINN-based Helmholtz solvers, their large training cost has been the main impediment...
Recently, researchers have explored the potential of physics-informed neural networks (PINNs) in solving the Helmholtz equation with limited success. While a number of attractive features have been demonstrated for the PINN-based Helmholtz solvers, their large training time has been the main impediment...
The Chen-Lee-Liu equationWe consider the exact rogue periodic wave (rogue wave on the periodic background) and periodic wave solutions for the Chen-Lee-Liu equation via the odd-th order Darboux transformation. Then, the multi-layer physics-informed neural networks (PINNs) deep learning method ...
The proposed 2W-PE method has high computational accuracy and efficiency, which reflects the applicability of machine learning in solving the computational efficiency problem of radio wave propagation. Therefore, this study provides a very effective and reliable method for solving the spatial field in ...
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 2019, 378, 686–707. [Google Scholar] [CrossRef] Kelley, H.J. Gradient theory of optimal flight paths. Ars J. 1960, 30, ...
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 2019, 378, 686–707. [Google Scholar] [CrossRef] Kelley, H.J. Gradient theory of optimal flight paths. Ars J. 1960, 30, ...