# Molecular Energy Learning Using Alternative Blackbox Matrix-Matrix Multiplication Algorithm for Exact Gaussian Process

arXiv: https://arxiv.org/abs/2109.09817 · HTML: https://mlsanity.com/paper/2109.09817/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 20 Sep 2021.

## Builds on (most cited first, 6 of 6)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Exact Gaussian Processes on a Million Data Points](https://mlsanity.com/paper/1903.08114/) (2019)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Preconditioning Kernel Matrices](https://mlsanity.com/paper/1602.06693/) (2016)
- [A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules](https://mlsanity.com/paper/1901.03309/) (2019)

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

- [Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space](https://mlsanity.com/paper/2204.09831/) (2022)
- [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 present an application of the blackbox matrix-matrix multiplication (BBMM) algorithm to scale up the Gaussian Process (GP) training of molecular energies in the molecular-orbital based machine learning (MOB-ML) framework. An alternative implementation of BBMM (AltBBMM) is also proposed to train more efficiently (over four-fold speedup) with the same accuracy and transferability as the original BBMM implementation. The training of MOB-ML was limited to 220 molecules, and BBMM and AltBBMM scale the training of MOB-ML up by over 30 times to 6500 molecules (more than a million pair energies). The accuracy and transferability of both algorithms are examined on the benchmark datasets of organic molecules with 7 and 13 heavy atoms. These lower-scaling implementations of the GP preserve the state-of-the-art learning efficiency in the low-data regime while extending it to the large-data regime with better accuracy than other available machine learning works on molecular energies.