We present 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 wavefunction 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. Our result suggests that hydrogen in the planetary condition is even denser compared to previous Monte Carlo and ab initio molecular dynamics data, which is further away from the empirical chemical model predictions. Obtaining reliable equations of state of dense hydrogen, and in particular, direct access to entropy and free energy opens new opportunities in planetary modeling and high-pressure physics research.
翻译:我们对密度氢的方程采用了一种基于深度基因模型的无变能变化模型方法。我们使用一个正常流网络来模拟质子波尔兹曼分布,并使用一个风速神经网络来模拟质子位置的电子波功能。通过共同优化两个神经网络,我们达到了与先前的混合电离蒙特卡洛计算方法类似的无变能。我们的结果显示,行星状态中的氢比以前的蒙特卡洛和初始分子动态数据更稠密,这离实验化学模型预测更远。获得密度氢状态的可靠方程式,特别是直接获得环流和自由能源,为行星模型和高压物理学研究提供了新的机会。