The nonlinear dimer obtained through the nonlinear Schrödinger equation has been a workhorse for the discovery the role nonlinearity plays in strongly interacting systems. While the analysis of the stationary states demonstrates the onset of a symmetry broken state for some degree of nonlinearity, the full dynamics maps the system into an effective ϕ4 model. In this later context, the self-trapping transition is an initial condition-dependent transfer of a classical particle over a barrier set by the nonlinear term. This transition that has been investigated analytically and mathematically is expressed through the hyperbolic limit of Jacobian elliptic functions. The aim of this work is to recapture this transition through the use of methods of Artificial Intelligence (AI). Specifically, we used a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition and its dependence on initial conditions. Exploitation of this result in the case of the nondegenerate nonlinear dimer gives additional information on the more general dynamics and helps delineate linear from nonlinear localization. This work shows how AI methods may be embedded in physics and provide useful tools for discovery.

中文翻译：

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突破人工智能的动态对称性：二聚体自陷跃迁

通过非线性薛定谔方程获得的非线性二聚体一直是发现非线性在强相互作用系统中所起的作用的主力。虽然对静止状态的分析表明了某种程度的非线性对称破坏状态的开始，但完整的动力学将系统映射到一个有效的φ4模型。在后面的上下文中，自陷转换是经典粒子在非线性项设置的障碍上的初始条件相关转移。这种经过分析和数学研究的转变通过雅可比椭圆函数的双曲极限来表示。这项工作的目的是通过使用人工智能 (AI) 的方法来重新捕捉这种转变。具体来说，我们使用了一个物理驱动的机器学习模型，该模型被证明能够捕获原始的动态自陷转换及其对初始条件的依赖性。在非简并非线性二聚体的情况下利用这一结果可以提供更多关于更一般动力学的信息，并有助于从非线性定位中描绘线性。