多任务神经网络对原子核低激发谱的研究

原子核低激发谱对深入理解原子核结构具有重要作用。采用多任务反向传播(Back Propagation,BP)的神经网络方法系统研究了原子核2 ₁⁺和4 ₁⁺的激发能量。除了质子数和中子数外，通过在网络输入层增加一个有关原子核集体性的物理量，BP神经网络在0.1 MeV到数MeV的能量范围内很好地拟合了原子核的低激发能。相比五维集体哈密顿量(Five-Dimensional Collective Hamiltonian,5DCH)方法，BP神经网络更好地再现了原子核低激发能的同位素趋势，以及由壳效应导致的幻数原子核低激发能的突然增大，并且将2 ₁⁺和4₁⁺激发能的预言精度分别提高了约80%和75%，该预言精度与单任务神经网络基本一致，但是改进了对轻核区与缺中子核区低激发谱的学习能力，这说明多任务神经网络可以实现多种激发能量的统一精确计算。

Studies of Nuclear Low-lying Excitation Spectra with Multi-task Neural Network

The nuclear low-lying excitation spectra are very important for understanding nuclear structure. The excitation energies of $ {2}_{1}^{+} $ and $ {4}_{1}^{+} $ states are systematically studied by using the multi-task Back Propagation(BP) neural network method. The BP neural network can well fit the low-lying excitation energies in a large energy range from about 0.1 MeV to about several MeV, by including a physical quantity related to nuclear collectivity on input layer besides proton and neutron numbers. Compared with the five-dimensional Collective Hamiltonian(5DCH) method, BP neural network can better reproduce the isotope trend of low excitation energy of nuclei, including the rapid increase of low excitation energy of magic nuclei caused by shell effect. The prediction accuracy for $ {2}_{1}^{+} $ and $ {4}_{1}^{+} $ states is improved by about 80% and 75%, respectively, which are similar to those of single-task neural network, while the learning ability for low excitation spectra in light and neutron-deficient nuclei is improved, indicating that multi-task neural network can achieve a unified and precise calculation of multiple excitation energies.