论文标题
数据驱动的孤子解决方案和非线性波模型的模型参数通过保护法约束神经网络方法
Data-driven soliton solutions and model parameters of nonlinear wave models via the conservation-law constrained neural network method
论文作者
论文摘要
在深度学习的过程中，我们将非线性波模型的更具集成信息（例如从整合理论获得的保护定律）整合到神经网络结构中，并提出一种保护律的神经网络方法与灵活的学习率约束神经网络方法，以预测非线性波模型的解决方案和参数。作为一些示例，我们研究了实际且复杂的典型非线性波模型，包括非线性Schrödinger方程，Korteweg-de Vries和改进的Korteweg-De Vries方程。与传统物理信息的神经网络方法相比，这种新方法即使在没有边界条件的情况下，即使需要较少的信息，也可以更准确地预测某些特定非线性波模型的解决方案和参数。这通过结合深度学习和综合理论来参考非线性波模型的进一步研究解决方案。
In the process of the deep learning, we integrate more integrable information of nonlinear wave models, such as the conservation law obtained from the integrable theory, into the neural network structure, and propose a conservation-law constrained neural network method with the flexible learning rate to predict solutions and parameters of nonlinear wave models. As some examples, we study real and complex typical nonlinear wave models, including nonlinear Schrödinger equation, Korteweg-de Vries and modified Korteweg-de Vries equations. Compared with the traditional physics-informed neural network method, this new method can more accurately predict solutions and parameters of some specific nonlinear wave models even when less information is needed, for example, in the absence of the boundary conditions. This provides a reference to further study solutions of nonlinear wave models by combining the deep learning and the integrable theory.
