利用可微规划获得能量和密度优化的交换相关泛函
Using differentiable programming to obtain an energy and density-optimized exchange-correlation functional
摘要：
使用端到端的可微实现的Kohn-Sham自洽场方程，我们得到一个精确的基于神经网络的电子密度的交换和相关（XC）泛函。使用能量和密度的信息来优化泛函，同时通过适当的神经网络架构来执行精确的约束。我们评估我们的模型对不同的家庭XC近似，并表明，对于非经验泛函，有很强的能量和密度误差之间的线性相关性。我们使用这种相关性来定义一种新的XC功能质量度量，其中包括能量和密度误差，从而导致一种新的，改进的方式来排名不同的近似。根据这个指标判断，我们的机器学习函数显著优于相同近似范围内的函数。
英文摘要：
Using an end-to-end differentiable implementation of the Kohn-Sham self-consistent field equations, we obtain an accurate neural network-based exchange and correlation (XC) functional of the electronic density. The functional is optimized using information on both energy and density while exact constraints are enforced through an appropriate neural network architecture. We evaluate our model against different families of XC approximations and show that, for non-empirical functionals, there is a strong linear correlation between energy and density errors. We use this correlation to define a novel XC functional quality metric that includes both energy and density errors, leading to a new, improved way to rank different approximations. Judged by this metric, our machine-learned functional significantly outperforms those within the same rung of approximations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
