论文标题
机器学习扩散蒙特卡洛能量
Machine Learning Diffusion Monte Carlo Energies
论文作者
论文摘要
我们提出了两种能够用小数据集预测扩散蒙特卡洛（DMC）能量的机器学习方法（总计约60 dmc计算）。首先使用Voxel深神经网络（VDNN）使用Kohn-Sham密度功能理论（DFT）电子密度作为输入来预测DMC能量密度。第二种使用内核脊回归（KRR）来预测使用原子环境矢量作为输入对DMC总能量的原子贡献（我们使用了原子中心的对称函数，来自ANI模型的原子环境矢量以及原子位置的平滑重叠）。我们首先比较了原始石墨烯晶格的方法论，在该方法中，我们发现KRR方法与梯度增强的决策树，随机森林，高斯工艺回归和多层感知器相比，krr方法的表现最佳。另外，KRR的表现优于VDNNS。之后，我们研究了KRR预测与石器缺陷相关的能屏障的普遍性。最后，我们从2D材料移至3D材料，并使用KRR预测液态水的总能量。在所有情况下，我们都会发现KRR模型比Kohn-Sham DFT更准确，并且所有的绝对误差都小于化学精度。
We present two machine learning methodologies that are capable of predicting diffusion Monte Carlo (DMC) energies with small datasets (~60 DMC calculations in total). The first uses voxel deep neural networks (VDNNs) to predict DMC energy densities using Kohn-Sham density functional theory (DFT) electron densities as input. The second uses kernel ridge regression (KRR) to predict atomic contributions to the DMC total energy using atomic environment vectors as input (we used atom centred symmetry functions, atomic environment vectors from the ANI models, and smooth overlap of atomic positions). We first compare the methodologies on pristine graphene lattices, where we find the KRR methodology performs best in comparison to gradient boosted decision trees, random forest, gaussian process regression, and multilayer perceptrons. In addition, KRR outperforms VDNNs by an order of magnitude. Afterwards, we study the generalizability of KRR to predict the energy barrier associated with a Stone-Wales defect. Lastly, we move from 2D to 3D materials and use KRR to predict total energies of liquid water. In all cases, we find that the KRR models are more accurate than Kohn-Sham DFT and all mean absolute errors are less than chemical accuracy.
