Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones
Data-driven localized waves and parameter discovery in the massive Thirring model via extended physics-informed neural networks with interface zones
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DOI：
10.1016/j.chaos.2023.114090
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发表时间：
2023-09
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影响因子：
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通讯作者：
Junchao Chen;Jin Song;Zijian Zhou;Zhenya Yan
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文献类型：
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作者：
Junchao Chen;Jin Song;Zijian Zhou;Zhenya Yan
在本文中，我们研究了数据驱动的局域波解和参数发现的大规模Thirring（MT）模型通过深度学习的框架下的物理信息神经网络（PINNs）算法。对明/暗型孤立子、呼吸子和流氓波等丰富的数据驱动解进行了准确的模拟，并对相对误差和绝对误差进行了对比分析。对于高阶局域波解，我们采用扩展PINNs（XPINNs）与区域分解捕捉完整的图片的动力学行为，如孤子碰撞，呼吸振荡和流氓波叠加。特别是，我们修改的界面线区域分解的XPINNs到一个小的接口区，并引入伪初始，残差和梯度条件作为接口条件连接相邻的个别神经网络。然后将这种改进的方法成功地应用于各种解，包括亮-亮孤子、暗-暗孤子、暗-反暗孤子、一般呼吸子、Kuznetsov-Ma呼吸子和二阶流氓波。实验结果表明，改进后的XPINNs在保持学习解质量的同时，具有更快的收敛速度，降低了计算复杂度。对于反问题，采用经典的PINNs算法，在有噪声和无噪声的情况下，精确地识别MT模型中线性和非线性项的未知系数参数。
In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm.