Xie Hao, Li Zi-Hang, Wang Han, Zhang Linfeng, Wang Lei
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China.
Phys Rev Lett. 2023 Sep 22;131(12):126501. doi: 10.1103/PhysRevLett.131.126501.
We developed a deep generative model-based variational free energy approach to the equations of state of dense hydrogen. We employ a normalizing flow network to model the proton Boltzmann distribution and a fermionic neural network to model the electron wave function at given proton positions. By jointly optimizing the two neural networks we reached a comparable variational free energy to the previous coupled electron-ion Monte Carlo calculation. The predicted equation of state of dense hydrogen under planetary conditions is denser than the findings of ab initio molecular dynamics calculation and empirical chemical model. Moreover, direct access to the entropy and free energy of dense hydrogen opens new opportunities in planetary modeling and high-pressure physics research.
我们开发了一种基于深度生成模型的变分自由能方法来研究致密氢的状态方程。我们使用归一化流网络来模拟质子玻尔兹曼分布，并使用费米子神经网络来模拟给定质子位置处的电子波函数。通过联合优化这两个神经网络，我们得到了与之前的耦合电子-离子蒙特卡罗计算相当的变分自由能。预测的行星条件下致密氢的状态方程比从头算分子动力学计算和经验化学模型的结果密度更大。此外，直接获取致密氢的熵和自由能为行星建模和高压物理研究开辟了新的机会。
