机器学习加速CALYPSO结构预测的可行性

doi:10.13229/j.cnki.jdxbgxb20191070

摘要/Abstract

摘要：

对机器学习替代DFT能量计算方法加速CALYPSO结构预测进行研究，选择5种机器学习方法评估其预测硼团簇总能量时的性能。使用库伦矩阵把原始数据表征为结构信息矩阵，提取矩阵特征值向量作为算法输入输出来训练模型；采用相同数据集评估算法，并探索影响算法性能的其他因素。提出基于势能面特征的相似性判断方法，建立置信度模型对性能最佳算法进行验证，结果表明：核岭回归算法预测出的势能面和DFT具有相似性；当允许误差为1 kcal/mol时，算法置信度接近90%。时间测试结果显示，核岭回归算法时间复杂度为 $Ο (n)$ ，比DFT方法提高1~2个数量级。

关键词: 计算机应用, 结构预测, 能量计算, 均方根误差, 置信度

Abstract:

The potential of accelerating CALYPSO structure prediction by replacing DFT methods with machine learning was studied. The performance in predicting the potential energy of boron clusters was evaluated with five machine learning methods. Firstly， the original data was represented as structural information metrics with Coulomb matrix. Then the eigenvalue vector pair of the matrix was extracted and used as the input of machine learning algorithms to training model， five algorithms were trained and tested using the same dataset. Also， factors affecting the performance were explored. Finally， a method of comparing the similarity of predicted values and ground truth was proposed based on the characters of potential energy surface （PES）， and a confidence model was constructed to validate the best kernel ridge regression （KRR） method. It is suggested that PES fitted by KRR is similar with the PES by DFT， and the confidence of the algorithm is closed to 90% while permissible error is 1 kcal/mol. The result of time test to KRR shows that the method’s time complexity is O（n）， which is improved by 1 to 2 orders of magnitude compared with DFT methods.

Key words: computer application, structure prediction, energy calculation, root mean square error, confidence

中图分类号:

TP399

魏晓辉,周长宝,沈笑先,刘圆圆,童群超. 机器学习加速CALYPSO结构预测的可行性[J]. 吉林大学学报(工学版), 2021, 51(2): 667-676.

Xiao-hui WEI,Chang-bao ZHOU,Xiao-xian SHEN,Yuan-yuan LIU,Qun-chao TONG. Accelerating CALYPSO structure prediction with machine learning[J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(2): 667-676.

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X	Y	Z
能量：-123.82 eV
12.36	13.54	6.50
6.84	6.45	6.50
10.66	10.95	6.49
8.18	9.27	6.49

项目	训练时间/ms	预测时间/ms
KNN	29.02	76.49
KRR	13 777.21	2 157.36
LRR	10.34	0.5
MNN	4 403.28	5.46
SVR	14 404.39	2 408.4

允许误差	B₂₀	B₂₂	B₂₄	B₂₈	B₃₀	B₃₆	B₃₈	B₄₀
0.50	0.666	0.655	0.721	0.769	0.732	0.756	0.752	0.767
0.55	0.709	0.710	0.753	0.793	0.754	0.766	0.773	0.795
0.60	0.745	0.754	0.780	0.809	0.786	0.797	0.801	0.832
0.65	0.767	0.782	0.805	0.829	0.808	0.810	0.809	0.852
0.70	0.790	0.802	0.816	0.849	0.840	0.834	0.835	0.866
0.75	0.803	0.833	0.836	0.869	0.855	0.844	0.850	0.881
0.80	0.815	0.845	0.854	0.880	0.874	0.864	0.860	0.895
0.85	0.825	0.877	0.872	0.884	0.874	0.878	0.868	0.908
0.90	0.845	0.885	0.877	0.896	0.882	0.885	0.877	0.919
0.95	0.858	0.893	0.885	0.900	0.887	0.905	0.884	0.924
1.00	0.862	0.897	0.891	0.900	0.894	0.915	0.888	0.929