论文标题
通过深度学习，用对数非线性schrodinger方程来解决对数非线性schrodinger方程的前进和反问题
Solving forward and inverse problems of the logarithmic nonlinear Schrodinger equation with PT-symmetric harmonic potential via deep learning
论文作者
论文摘要
在本文中，我们研究了具有平等时间（PT） - 对称谐波电位的对数非线性Schrödinger（LNLS）方程，这在许多领域中都是核物理，量子光学，岩浆转运现象和有效量子重力等许多领域的重要物理模型。选择了三种类型的初始值条件和周期性边界条件，以通过物理知识的神经网络（PINN）深度学习方法用PT-对称谐波电位求解LNLS方程，并将这些获得的结果与从傅立叶光谱方法中得出的结果进行比较。此外，我们还通过选择独特的空间宽度或独特的优化步骤来研究PINLS方程对LNLS方程的有效性。最后，我们使用PINNS深度学习方法有效地解决了具有PT-对称谐波电位的LNLS方程发现的数据驱动的发现，从而大致发现分散系数和非线性项的系数或PT -Sym -Ammmetric谐波电位的幅度。
In this paper, we investigate the logarithmic nonlinear Schrödinger (LNLS) equation with the parity-time (PT)-symmetric harmonic potential, which is an important physical model in many fields such as nuclear physics, quantum optics, magma transport phenomena, and effective quantum gravity. Three types of initial value conditions and periodic boundary conditions are chosen to solve the LNLS equation with PT -symmetric harmonic potential via the physics-informed neural networks (PINNs) deep learning method, and these obtained results are compared with ones deduced from the Fourier spectral method. Moreover, we also investigate the effectiveness of the PINNs deep learning for the LNLS equation with PT symmetric potential by choosing the distinct space widths or distinct optimized steps. Finally, we use the PINNs deep learning method to effectively tackle the data-driven discovery of the LNLS equation with PT -symmetric harmonic potential such that the coefficients of dispersion and nonlinear terms or the amplitudes of PT -symmetric harmonic potential can be approximately found.
