Liang Xiao, Zhang Huan, Liu Sheng, Li Yan, Zhang Yong-Sheng
Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.
CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China.
Sci Rep. 2018 Nov 5;8(1):16337. doi: 10.1038/s41598-018-34725-9.
We show that both single-component and two-component Bose-Einstein condensates' (BECs) ground states can be simulated by a deep convolutional neural network. We trained the neural network via inputting the parameters in the dimensionless Gross-Pitaevskii equation (GPE) and outputting the ground-state wave function. After the training, the neural network generates ground-state wave functions with high precision. We benchmark the neural network for either inputting different coupling strength in the GPE or inputting an arbitrary potential under the infinite double walls trapping potential, and it is found that the ground state wave function generated by the neural network gives the relative chemical potential error magnitude below 10. Furthermore, the neural network trained with random potentials shows prediction ability on other types of potentials. Therefore, the BEC ground states, which are continuous wave functions, can be represented by deep convolutional neural networks.
我们表明，单组分和双组分玻色-爱因斯坦凝聚体（BECs）的基态都可以由深度卷积神经网络进行模拟。我们通过输入无量纲格罗斯-皮塔耶夫斯基方程（GPE）中的参数并输出基态波函数来训练神经网络。训练后，神经网络能高精度地生成基态波函数。我们对神经网络进行基准测试，测试内容为在GPE中输入不同的耦合强度，或在无限双壁捕获势下输入任意势，结果发现神经网络生成的基态波函数给出的相对化学势误差幅度低于10。此外，用随机势训练的神经网络对其他类型的势也具有预测能力。因此，作为连续波函数的BEC基态可以由深度卷积神经网络来表示。
