论文标题
使用深度学习方法的数据驱动的可变系数hirota方程的前进问题
Data-driven forward-inverse problems for the variable coefficients Hirota equation using deep learning method
论文作者
论文摘要
本文讨论了可变系数Hirota（VCH）方程的数据驱动的前向问题。主要思想是将改进的物理信息神经网络（IPINN）算法与局部自适应激活功能，坡度恢复项和参数正则化一起恢复数据驱动的孤子顿孔和VCH方程的高级孤子，并在初始结合条件下以及噪音驱动的参数中发现了不同的参数。数值结果表明可以证明两个事实：（i）通过调整网络层，神经元，原始训练数据，时空区域和iPinn算法的其他参数，可以成功地学习VCH方程的数据驱动的孤子解决方案； （ii）可以通过在IPINN算法中引入具有适当权重系数的参数正则化策略来稳定，准确地训练预测参数。在这项工作中获得的结果验证了IPINN算法在解决可变系数方程的前进问题方程的有效性。
Data-driven forward-inverse problems for the variable coefficients Hirota (VCH) equation are discussed in this paper. The main idea is to use the improved physics-informed neural networks (IPINN) algorithm with neuron-wise locally adaptive activation function, slope recovery term and parameter regularization to recover the data-driven solitons and high-order soliton of the VCH equation with initial-boundary conditions, as well as the data-driven parameters discovery for VCH equation with unknown parameters under noise of different intensity. Numerical results are shown to demonstrate two facts: (i) data-driven soliton solutions of the VCH equation are successfully learned by adjusting the network layers, neurons, the original training data, spatiotemporal regions and other parameters of the IPINN algorithm; (ii) the prediction parameter can be trained stably and accurately by introducing a parameter regularization strategy with an appropriate weight coefficients into the IPINN algorithm. The results achieved in this work verify the effectiveness of the IPINN algorithm in solving the forward-inverse problems of the variable coefficients equation.
