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

arXiv: https://arxiv.org/abs/2204.09831 · HTML: https://mlsanity.com/paper/2204.09831/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 75 references that are in the map.
- First posted on arXiv 21 Apr 2022.

## Builds on (most cited first, 15 of 15)

- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Learning to Plan Chemical Syntheses](https://mlsanity.com/paper/1708.04202/) (2017)
- [Deep Reinforcement Learning for De-Novo Drug Design](https://mlsanity.com/paper/1711.10907/) (2017)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Hierarchical modeling of molecular energies using a deep neural network](https://mlsanity.com/paper/1710.00017/) (2017)
- [Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra](https://mlsanity.com/paper/1705.05907/) (2017)
- [Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles](https://mlsanity.com/paper/2003.12437/) (2020)
- [Neural networks for the prediction organic chemistry reactions](https://mlsanity.com/paper/1608.06296/) (2016)
- [A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules](https://mlsanity.com/paper/1901.03309/) (2019)
- [A Fast Incremental Gaussian Mixture Model](https://mlsanity.com/paper/1506.04422/) (2015)
- [Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning](https://mlsanity.com/paper/1909.02041/) (2019)
- [Molecular Energy Learning Using Alternative Blackbox Matrix-Matrix Multiplication Algorithm for Exact Gaussian Process](https://mlsanity.com/paper/2109.09817/) (2021)

## Built on by (most cited first, 3 of 3)

- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)
- [Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learning](https://mlsanity.com/paper/2205.15510/) (2022)
- [Molecular-orbital-based Machine Learning for Open-shell and Multi-reference Systems with Kernel Addition Gaussian Process Regression](https://mlsanity.com/paper/2207.08317/) (2022)

## Abstract (arXiv)

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 [J. Chem. Theory Comput., 15, 6668 (2019)] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantage of accurately reproducing chemically intuitive groupings of frontier molecular orbitals and having improved performance with an increasing number of training examples. The resulting clusters from supervised or unsupervised clustering is 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 Gaussian process regression (GMM/GPR) is the most efficient training protocol for MOB-ML. The numerical tests of molecular energy learning on thermalized datasets of drug-like molecules demonstrate the improved accuracy, transferability, and learning efficiency of GMM/GPR over not only other training protocols for MOB-ML, i.e., supervised regression-clustering combined with GPR(RC/GPR) and GPR without clustering. GMM/GPR also provide the best molecular energy predictions compared with the ones from literature on the same benchmark datasets. 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.