Harnessing deep neural networks to solve inverse problems in quantum dynamics: machine-learned predictions of time-dependent optimal control fields
Harnessing deep neural networks to solve inverse problems in quantum dynamics: machine-learned predictions of time-dependent optimal control fields
复制标题
利用深度神经网络解决量子动力学中的逆问题：依赖时间的最优控制场的机器学习预测
DOI：
10.1039/d0cp03694c
复制
发表时间：
2020
影响因子：
3.3
通讯作者：
Wong, Bryan M.
中科院分区：
文献类型：
--
作者：
Wang, Xian;Kumar, Anshuman;Shelton, Christian R.;Wong, Bryan M.
逆问题在物理科学中继续获得巨大的兴趣，特别是在控制非平衡系统中的期望现象的背景下。在这项工作中，我们利用一系列深度神经网络来预测时间相关的最优控制场E（t），从而实现降维量子动力学系统中所需的电子跃迁。为了解决这个逆问题，我们研究了两种独立的机器学习方法：（1）用于预测频域中功率谱的频率和幅度内容的前馈神经网络（即，E（t）的傅立叶变换），以及（2）用于在时域中直接预测E（t）的互相关神经网络方法。这两种机器学习方法都提供了探索底层量子动力学的互补方法，并且在准确预测最优控制场的频率和强度方面表现出令人印象深刻的性能。我们为这些深度神经网络提供了详细的架构和超参数，以及每个机器学习模型的性能指标。从这些结果中，我们表明，机器学习，特别是深度神经网络，可以作为具有成本效益的统计方法，用于设计电磁场，以实现这些量子动力学系统中所需的转变。
Inverse problems continue to garner immense interest in the physical sciences, particularly in the context of controlling desired phenomena in non-equilibrium systems. In this work, we utilize a series of deep neural networks for predicting time-dependent optimal control fields, E(t), that enable desired electronic transitions in reduced-dimensional quantum dynamical systems. To solve this inverse problem, we investigated two independent machine learning approaches: (1) a feedforward neural network for predicting the frequency and amplitude content of the power spectrum in the frequency domain (i.e., the Fourier transform of E(t)), and (2) a cross-correlation neural network approach for directly predicting E(t) in the time domain. Both of these machine learning methods give complementary approaches for probing the underlying quantum dynamics and also exhibit impressive performance in accurately predicting both the frequency and strength of the optimal control field. We provide detailed architectures and hyperparameters for these deep neural networks as well as performance metrics for each of our machine-learned models. From these results, we show that machine learning, particularly deep neural networks, can be employed as cost-effective statistical approaches for designing electromagnetic fields to enable desired transitions in these quantum dynamical systems.