Kalita Bhupalee, Pederson Ryan, Chen Jielun, Li Li, Burke Kieron
Department of Chemistry, University of California, Irvine, California 92697, United States.
Department of Physics and Astronomy, University of California, Irvine, California 92697, United States.
J Phys Chem Lett. 2022 Mar 24;13(11):2540-2547. doi: 10.1021/acs.jpclett.2c00371. Epub 2022 Mar 14.
Kohn-Sham regularizer (KSR) is a differentiable machine learning approach to finding the exchange-correlation functional in Kohn-Sham density functional theory that works for strongly correlated systems. Here we test KSR for a weak correlation. We propose spin-adapted KSR (sKSR) with trainable local, semilocal, and nonlocal approximations found by minimizing density and total energy loss. We assess the atoms-to-molecules generalizability by training on one-dimensional (1D) H, He, Li, Be, and Be and testing on 1D hydrogen chains, LiH, BeH, and helium hydride complexes. The generalization error from our semilocal approximation is comparable to other differentiable approaches, but our nonlocal functional outperforms any existing machine learning functionals, predicting ground-state energies of test systems with a mean absolute error of 2.7 mH.
科恩-沈正则化器（KSR）是一种可微的机器学习方法，用于在科恩-沈密度泛函理论中寻找适用于强关联系统的交换关联泛函。在此，我们针对弱关联对KSR进行测试。我们提出了自旋适配的KSR（sKSR），通过最小化密度和总能量损失来找到可训练的局域、半局域和非局域近似。我们通过对一维（1D）的H、He、Li、Be以及Be进行训练，并对一维氢链、LiH、BeH和氢化氦配合物进行测试，来评估从原子到分子的泛化能力。我们半局域近似的泛化误差与其他可微方法相当，但我们的非局域泛函优于任何现有的机器学习泛函，预测测试系统的基态能量时平均绝对误差为2.7 mH。
