# Hierarchical modeling of molecular energies using a deep neural network

Source: [Hierarchical modeling of molecular energies using a deep neural network](<https://www.sota2.com/research/paper/68fa37711e209131ce8b26e6>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2026-01-01T02:16:06.548Z

Authors: Nicholas Lubbers, Justin S. Smith, Kipton Barros

Published: 2017-09-29T18:12:29.000Z

## Abstract

We introduce the Hierarchically Interacting Particle Neural Network (HIP-NN) to model molecular properties from datasets of quantum calculations. Inspired by a many-body expansion, HIP-NN decomposes properties, such as energy, as a sum over hierarchical terms. These terms are generated from a neural network--a composition of many nonlinear transformations--acting on a representation of the molecule. HIP-NN achieves state-of-the-art performance on a dataset of 131k ground state organic molecules, and predicts energies with 0.26 kcal/mol mean absolute error. With minimal tuning, our model is also competitive on a dataset of molecular dynamics trajectories. In addition to enabling accurate energy predictions, the hierarchical structure of HIP-NN helps to identify regions of model uncertainty.

## Recorded benchmark results

A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage.

- [Molecular Energy Prediction on QM9 50000 samples](<https://www.sota2.com/research/sota/molecular-energy-prediction-on-qm9-50000-samples.md>): Molecular energy prediction; QM9 50000 samples; MAE: 0.354.

- [Molecular Energy Prediction on QM9](<https://www.sota2.com/research/sota/molecular-energy-prediction-on-qm9.md>): Molecular energy prediction; QM9; MAE: 0.256.

- [Molecular Property Prediction on QM9 (test)](<https://www.sota2.com/research/sota/molecular-property-prediction-on-qm9-test.md>): Molecular property prediction; QM9 (test); mu: not recorded.

- [Energy and force prediction on MD17 Benzene (test)](<https://www.sota2.com/research/sota/energy-and-force-prediction-on-md17-benzene-test.md>): Energy and force prediction; MD17 Benzene (test); Energy MAE (kcal/mol): not recorded.

- [Energy and force prediction on MD17 Toluene (test)](<https://www.sota2.com/research/sota/energy-and-force-prediction-on-md17-toluene-test.md>): Energy and force prediction; MD17 Toluene (test); Energy MAE (kcal/mol): not recorded.

- [Energy and force prediction on MD17 Malonaldehyde (test)](<https://www.sota2.com/research/sota/energy-and-force-prediction-on-md17-malonaldehyde-test.md>): Energy and force prediction; MD17 Malonaldehyde (test); Energy MAE: not recorded.

- [Energy and force prediction on MD17 Salicylic acid (test)](<https://www.sota2.com/research/sota/energy-and-force-prediction-on-md17-salicylic-acid-test.md>): Energy and force prediction; MD17 Salicylic acid (test); Energy MAE (kcal/mol): not recorded.

## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1710.00017>)

[PDF](<https://arxiv.org/pdf/1710.00017.pdf>)