# The Many-Body Expansion Combined with Neural Networks

arXiv: https://arxiv.org/abs/1609.07072 · HTML: https://mlsanity.com/paper/1609.07072/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Sep 2016.

## Built on by (most cited first, 2 of 2)

- [Many-body Expansion Based Machine Learning Models for Octahedral Transition Metal Complexes](https://mlsanity.com/paper/2410.09659/) (2024)
- [Transferable FB-GNN-MBE Framework for Potential Energy Surfaces: Data-Adaptive Transfer Learning in Deep Learned Many-Body Expansion Theory](https://mlsanity.com/paper/2604.09320/) (2026)

## Abstract (arXiv)

Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of fragments required for chemical accuracy is still prohibitively expensive for ab-initio MBE to compete with force field approximations for applications beyond single-point energies. Alongside the MBE, empirical models of ab-initio potential energy surfaces have improved, especially non-linear models based on neural networks (NN) which can reproduce ab-initio potential energy surfaces rapidly and accurately. Although they are fast, NNs suffer from their own curse of dimensionality; they must be trained on a representative sample of chemical space. In this paper we examine the synergy of the MBE and NN's, and explore their complementarity. The MBE offers a systematic way to treat systems of arbitrary size and intelligently sample chemical space. NN's reduce, by a factor in excess of 106 the computational overhead of the MBE and reproduce the accuracy of ab-initio calculations without specialized force fields. We show they are remarkably general, providing comparable accuracy with drastically different chemical embeddings. To assess this we test a new chemical embedding which can be inverted to predict molecules with desired properties.