# Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learning

arXiv: https://arxiv.org/abs/2205.15510 · HTML: https://mlsanity.com/paper/2205.15510/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 78 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 21 of 21)

- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Optimization of Molecules via Deep Reinforcement Learning](https://mlsanity.com/paper/1810.08678/) (2018)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Deep Reinforcement Learning for De-Novo Drug Design](https://mlsanity.com/paper/1711.10907/) (2017)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [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)
- [Deep learning for molecular design - a review of the state of the art](https://mlsanity.com/paper/1903.04388/) (2019)
- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [Generative Models for Automatic Chemical Design](https://mlsanity.com/paper/1907.01632/) (2019)
- [Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles](https://mlsanity.com/paper/2003.12437/) (2020)
- [Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: Application to ternary random alloys](https://mlsanity.com/paper/2006.00139/) (2020)
- [A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules](https://mlsanity.com/paper/1901.03309/) (2019)
- [Multi-task learning for electronic structure to predict and explore molecular potential energy surfaces](https://mlsanity.com/paper/2011.02680/) (2020)
- [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)
- [Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space](https://mlsanity.com/paper/2204.09831/) (2022)

## Built on by (most cited first, 1 of 1)

- [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)

This study extends the accurate and transferable molecular-orbital-based machine learning (MOB-ML) approach to modeling the contribution of electron correlation to dipole moments at the cost of Hartree-Fock computations. A molecular-orbital-based (MOB) pairwise decomposition of the correlation part of the dipole moment is applied, and these pair dipole moments could be further regressed as a universal function of molecular orbitals (MOs). The dipole MOB features consist of the energy MOB features and their responses to electric fields. An interpretable and rotationally equivariant Gaussian process regression (GPR) with derivatives algorithm is introduced to learn the dipole moment more efficiently. The proposed problem setup, feature design, and ML algorithm are shown to provide highly-accurate models for both dipole moment and energies on water and fourteen small molecules. To demonstrate the ability of MOB-ML to function as generalized density-matrix functionals for molecular dipole moments and energies of organic molecules, we further apply the proposed MOB-ML approach to train and test the molecules from the QM9 dataset. The application of local scalable GPR with Gaussian mixture model unsupervised clustering (GMM/GPR) scales up MOB-ML to a large-data regime while retaining the prediction accuracy. In addition, compared with literature results, MOB-ML provides the best test MAEs of 4.21 mDebye and 0.045 kcal/mol for dipole moment and energy models, respectively, when training on 110000 QM9 molecules. The excellent transferability of the resulting QM9 models is also illustrated by the accurate predictions for four different series of peptides.