等离子体激元诱导透明中的非线性波学习
Learning Nonlinear Waves in Plasmon-induced Transparency
摘要：
等离子体激元诱导透明（PIT）表现出复杂的非线性动力学，在诸如非线性波等领域发现了临界现象。然而，这样的非线性解敏感地依赖于薛定谔方程中的参数和不同势的选择。尽管如此复杂，机器学习社区已经在通过回归预测复杂数据集方面取得了显着的效率。在这里，我们考虑一个递归神经网络（RNN）的方法来预测复杂的传播的非线性孤子在等离子体激元诱导的透明超材料系统与施加的电位绕过需要的分析和数值方法的指导模型。我们证明了该方案的成功预测的非线性孤子的传播仅从一个给定的初始条件和潜在的。我们证明了长短期记忆（LSTM）人工神经网络的模拟和预测结果的显着协议。该框架为RNN在量子系统和基于薛定谔方程的非线性波中的应用开辟了新的前景，例如冷原子系统和非线性纤维光学中的非线性动力学。
英文摘要：
Plasmon-induced transparency (PIT) displays complex nonlinear dynamics that find critical phenomena in areas such as nonlinear waves. However, such a nonlinear solution depends sensitively on the selection of parameters and different potentials in the Schrödinger equation. Despite this complexity, the machine learning community has developed remarkable efficiencies in predicting complicated datasets by regression. Here, we consider a recurrent neural network (RNN) approach to predict the complex propagation of nonlinear solitons in plasmon-induced transparency metamaterial systems with applied potentials bypassing the need for analytical and numerical approaches of a guiding model. We demonstrate the success of this scheme on the prediction of the propagation of the nonlinear solitons solely from a given initial condition and potential. We prove the prominent agreement of results in simulation and prediction by long short-term memory (LSTM) artificial neural networks. The framework presented in this work opens up a new perspective for the application of RNN in quantum systems and nonlinear waves using Schrödinger-type equations, for example, the nonlinear dynamics in cold-atom systems and nonlinear fiber optics.
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