论文标题
通过深度学习方法，数据驱动的解决方案和非本地MKDV方程的参数发现
Data driven solutions and parameter discovery of the nonlocal mKdV equation via deep learning method
论文作者
论文摘要
在本文中，我们系统地研究了非本地MKDV方程的整合性和数据驱动的解决方案。非局部MKDV方程的无限保护定律和相应的无限保护量是通过Riccti方程提供的。通过使用多层物理信息神经网络算法研究了非局部MKDV方程的零边界的数据驱动解决方案，其中包括Kink Soliton，Complect Soliton，Bright-Bright-Bright Soliton以及Soliton和Soliton和kink-type之间的相互作用。对于具有非零边界的数据驱动的解决方案，我们研究扭结，黑暗，反黑和理性解决方案。通过图像模拟，给出了这些解决方案的相关动态行为和误差分析。此外，我们通过应用物理知识的神经网络算法来发现方程式的非线性项的参数，讨论了可集成的非局部MKDV方程的反问题。
In this paper, we systematically study the integrability and data-driven solutions of the nonlocal mKdV equation. The infinite conservation laws of the nonlocal mKdV equation and the corresponding infinite conservation quantities are given through Riccti equation. The data driven solutions of the zero boundary for the nonlocal mKdV equation are studied by using the multi-layer physical information neural network algorithm, which including kink soliton, complex soliton, bright-bright soliton and the interaction between soliton and kink-type. For the data-driven solutions with non-zero boundary, we study kink, dark, anti-dark and rational solution. By means of image simulation, the relevant dynamic behavior and error analysis of these solutions are given. In addition, we discuss the inverse problem of the integrable nonlocal mKdV equation by applying the physics-informed neural network algorithm to discover the parameters of the nonlinear terms of the equation.
