Predicting Molecular Energy Using Force-Field Optimized Geometries and Atomic Vector Representations Learned from an Improved Deep Tensor Neural Network.

The use of neural networks to predict molecular properties calculated from high level quantum mechanical calculations has made significant advances in recent years, but most models need input geometries from DFT optimizations which limit their applicability in practice. In this work, we explored how machine learning can be used to predict molecular atomization energies and conformation stability using optimized geometries from Merck Molecular Force Field (MMFF). On the basis of the recently introduced deep tensor neural network (DTNN) approach, we first improved its training efficiency and performed an extensive search of its hyperparameters, and developed a DTNN_7ib model which has a test accuracy of 0.34 kcal/mol mean absolute error (MAE) on QM9 data set. Then using atomic vector representations in the DTNN_7ib model, we employed transfer learning (TL) strategy to train readout layers on the QM9 data set, in which QM properties are the same as in QM9 [calculated at the B3LYP/6-31G(2df,p) level] while molecular geometries are corresponding local minima optimized with MMFF94 force field. The developed TL_QM9 model can achieve an MAE of 0.79 kcal/mol using MMFF optimized geometries. Furthermore, we demonstrated that the same transfer learning strategy with the same atomic vector representation can be used to develop a machine learning model that can achieve an MAE of 0.51 kcal/mol in molecular energy prediction using MMFF geometries for an eMol9_C conformation data set, which consists of 9959 molecules and 88 234 conformations with energies calculated at the B3LYP/6-31G* level. Our results indicate that DFT-level accuracy of molecular energy prediction can be achieved using force-field optimized geometries and atomic vector representations learned from deep tensor neural network, and integrated molecular modeling and machine learning would be a promising approach to develop more powerful computational tools for molecular conformation analysis.