用多级组合技术提升量子机器学习模型：Pople图再访
Boosting quantum machine learning models with multi-level combination technique: Pople diagrams revisited
摘要：
受量子化学中流行的Pople图的启发，我们引入了一种基于多级组合（C）技术的分层方案，以结合量子化学中计算分子能量时所做的各种近似。当与量子机器学习（QML）模型相结合时，所得到的CQML模型是一种广义统一递归核岭回归，它利用了在由多个维度的多个水平组成的训练数据中隐式编码的相关性。在这里，我们已经研究了三个维度：化学空间，基组和电子相关处理。对一组含有CHONFClS的至多7个原子（不计氢原子）的$\sim$ 7 '000有机分子以及C-$_7$ H $_{10}$ O $_2$的$\sim$ 6' 000结构异构体的原子化能进行了数值计算.原子化能量的CQML学习曲线表明，使用最准确和最昂贵的方法计算的必要训练样本大大减少。为了生成CCSD（T）/cc-pvdz原子化能量的毫秒估计值，预测误差达到化学精度（$\sim$ 1 kcal/mol），CQ ML模型在CCSD（T）/cc-pvdz水平下仅需要$\sim$ 100个训练实例，而不是传统QML中的数千个，而在较低水平下需要更多的训练分子。我们的结果表明，各种分层近似之间可能存在有利的权衡，其计算成本随电子数的变化而不同。
英文摘要：
Inspired by Pople diagrams popular in quantum chemistry, we introduce a hierarchical scheme, based on the multi-level combination (C) technique, to combine various levels of approximations made when calculating molecular energies within quantum chemistry. When combined with quantum machine learning (QML) models, the resulting CQML model is a generalized unified recursive kernel ridge regression which exploits correlations implicitly encoded in training data comprised of multiple levels in multiple dimensions. Here, we have investigated up to three dimensions: Chemical space, basis set, and electron correlation treatment. Numerical results have been obtained for atomization energies of a set of $\sim$7'000 organic molecules with up to 7 atoms (not counting hydrogens) containing CHONFClS, as well as for $\sim$6'000 constitutional isomers of C$_7$H$_{10}$O$_2$. CQML learning curves for atomization energies suggest a dramatic reduction in necessary training samples calculated with the most accurate and costly method. In order to generate milli-second estimates of CCSD(T)/cc-pvdz atomization energies with prediction errors reaching chemical accuracy ($\sim$1 kcal/mol), the CQML model requires only $\sim$100 training instances at CCSD(T)/cc-pvdz level, rather than thousands within conventional QML, while more training molecules are required at lower levels. Our results suggest a possibly favourable trade-off between various hierarchical approximations whose computational cost scales differently with electron number.
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