标题： 非弹性散射，通过保守和非保守物理信息神经网络在 Zakharov-Kuznetsov 方程中孤子的涌现相互作用 显示英文标题

标题： Inelastic Scattering, Emergent Interactions of Solitons in the Zakharov-Kuznetsov Equation through Conservative and non-Conservative Physics-Informed Neural Networks

摘要： Zakharov-Kuznetsov方程，最初是一个具有均匀磁场的等离子体的三维数学模型，是KdV方程向高维的直接扩展，是一个典型的准可积系统。 物理信息神经网络（PINNs）被用于研究2+1维Zakharov-Kuznetsov方程中的孤子解碰撞。 PINNs能够成功地在正向过程中求解方程，解是通过无网格方法和自动微分获得的，并考虑了守恒定律。 在反向过程中，可以从给定的训练数据中成功推导出方程的正确形式。 然而，在碰撞过程中情况变得难以处理。 正向分析结果不再遵循守恒定律，与其说是系统的解，不如说是一种动态不相容场配置（DIFC）。 因此，引入了守恒PINNs，本文我们成功获得了满足守恒定律的解。 反向分析表明存在一个不同的方程，其中系数表现出显著变化，这意味着出现了临时相互作用。 利用这些调制后的系数，我们重新计算了方程，并确认对守恒定律的遵守无疑得到了显著改善。 显示英文摘要

摘要： The Zakharov-Kuznetsov equation, originally a three dimensional mathematical model of plasma with a uniform magnetic field, is a direct extension of the KdV equation into higher dimensions and is a typical quasi-integrable system. Physics-Informed Neural Networks (PINNs) are used to study the collision of soliton solutions in the 2+1 dimensional Zakharov-Kuznetsov equation. PINNs are able to successfully solve the equations in the forward process, and the solutions are obtained using a mesh-free approach and automatic differentiation, taking into account conservation laws. In the inverse process, the proper form of the equation can be successfully derived from a given training data. However, the situation becomes intractable in the collision process. The forward analysis result no longer adheres to the laws of conservation, and is better described as a dynamically incompatible field configuration (DIFC) than a solution to the system. Conservative PINNs have thus been introduced for this purpose, and in this paper we succeed in obtaining solutions that satisfy conservation laws. The inverse analysis suggests a different equation in which the coefficients exhibit significant changes, implying an emergence of temporary interactions. With these modulated coefficients, we recalculate the equation and confirm that the adherence to the laws of conservation has unquestionably improved.