Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space.

We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM) in an entirely automatic manner and simplifies an earlier supervised clustering approach [ 2019, 15, 6668] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantages of accurately reproducing chemically intuitive groupings of frontier molecular orbitals and exhibiting improved performance with an increasing number of training examples. The resulting clusters from supervised or unsupervised clustering are further combined with scalable Gaussian process regression (GPR) or linear regression (LR) to learn molecular energies accurately by generating a local regression model in each cluster. Among all four combinations of regressors and clustering methods, GMM combined with scalable exact GPR (GMM/GPR) is the most efficient training protocol for MOB-ML. The numerical tests of molecular energy learning on thermalized data sets of drug-like molecules demonstrate the improved accuracy, transferability, and learning efficiency of GMM/GPR over other training protocols for MOB-ML, i.e., supervised regression clustering combined with GPR (RC/GPR) and GPR without clustering. GMM/GPR also provides the best molecular energy predictions compared with ones from the literature on the same benchmark data sets. With a lower scaling, GMM/GPR has a 10.4-fold speedup in wall-clock training time compared with scalable exact GPR with a training size of 6500 QM7b-T molecules.