# Hierarchical modeling of molecular energies using a deep neural network

arXiv: https://arxiv.org/abs/1710.00017 · HTML: https://mlsanity.com/paper/1710.00017/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2017.

## Built on by (most cited first, 30 of 37)

- [MACE: Higher Order Equivariant Message Passing Neural Networks for Fast and Accurate Force Fields](https://mlsanity.com/paper/2206.07697/) (2022)
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- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
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- [Denoise Pretraining on Nonequilibrium Molecules for Accurate and Transferable Neural Potentials](https://mlsanity.com/paper/2303.02216/) (2023)
- [Data efficiency and extrapolation trends in neural network interatomic potentials](https://mlsanity.com/paper/2302.05823/) (2023)
- [Fast and Sample-Efficient Interatomic Neural Network Potentials for Molecules and Materials Based on Gaussian Moments](https://mlsanity.com/paper/2109.09569/) (2021)
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- [FeNNol: an Efficient and Flexible Library for Building Force-field-enhanced Neural Network Potentials](https://mlsanity.com/paper/2405.01491/) (2024)
- [Projected Hessian Learning: Fast Curvature Supervision for Accurate Machine-Learning Interatomic Potentials](https://mlsanity.com/paper/2603.04523/) (2026)
- [Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space](https://mlsanity.com/paper/2204.09831/) (2022)
- [Extreme Acceleration of Graph Neural Network-based Prediction Models for Quantum Chemistry](https://mlsanity.com/paper/2211.13853/) (2022)
- [Synthetic data enable experiments in atomistic machine learning](https://mlsanity.com/paper/2211.16443/) (2022)
- [Equivariant Spherical Transformer for Efficient Molecular Modeling](https://mlsanity.com/paper/2505.23086/) (2025)
- [A Universal Framework for Featurization of Atomistic Systems](https://mlsanity.com/paper/2102.02390/) (2021)
- [Reconstructing Kernel-based Machine Learning Force Fields with Super-linear Convergence](https://mlsanity.com/paper/2212.12737/) (2022)
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- [Thermodynamic Transferability in Coarse-Grained Force Fields using Graph Neural Networks](https://mlsanity.com/paper/2406.12112/) (2024)
- [FastCHGNet: Training one Universal Interatomic Potential to 1.5 Hours with 32 GPUs](https://mlsanity.com/paper/2412.20796/) (2024)
- [Detect the Interactions that Matter in Matter: Geometric Attention for Many-Body Systems](https://mlsanity.com/paper/2106.02549/) (2021)
- [EcoFlow: Efficient Convolutional Dataflows for Low-Power Neural Network Accelerators](https://mlsanity.com/paper/2202.02310/) (2022)
- [Multi-Task Mixture Density Graph Neural Networks for Predicting Cu-based Single-Atom Alloy Catalysts for CO2 Reduction Reaction](https://mlsanity.com/paper/2209.07300/) (2022)
- [Artificial Intelligence in Material Engineering: A review on applications of AI in Material Engineering](https://mlsanity.com/paper/2209.11234/) (2022)
- [PANNA 2.0: Efficient neural network interatomic potentials and new architectures](https://mlsanity.com/paper/2305.11805/) (2023)
- [From Peptides to Nanostructures: A Euclidean Transformer for Fast and Stable Machine Learned Force Fields](https://mlsanity.com/paper/2309.15126/) (2023)
- [Optimal Invariant Bases for Atomistic Machine Learning](https://mlsanity.com/paper/2503.23515/) (2025)
- [A2I Transformer: Permutation-equivariant attention network for pairwise and many-body interactions with minimal featurization](https://mlsanity.com/paper/2110.14374/) (2021)

## Abstract (arXiv)

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.