# Fast and Sample-Efficient Interatomic Neural Network Potentials for Molecules and Materials Based on Gaussian Moments

arXiv: https://arxiv.org/abs/2109.09569 · HTML: https://mlsanity.com/paper/2109.09569/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 77 references that are in the map.
- First posted on arXiv 20 Sep 2021.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Wide Neural Networks of Any Depth Evolve as Linear Models Under Gradient Descent](https://mlsanity.com/paper/1902.06720/) (2019)
- [On Lazy Training in Differentiable Programming](https://mlsanity.com/paper/1812.07956/) (2018)
- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [On Exact Computation with an Infinitely Wide Neural Net](https://mlsanity.com/paper/1904.11955/) (2019)
- [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)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Less is more: sampling chemical space with active learning](https://mlsanity.com/paper/1801.09319/) (2018)
- [Hierarchical modeling of molecular energies using a deep neural network](https://mlsanity.com/paper/1710.00017/) (2017)
- [Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation](https://mlsanity.com/paper/1810.11890/) (2018)
- [Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra](https://mlsanity.com/paper/1705.05907/) (2017)
- [Gaussian Moments as Physically Inspired Molecular Descriptors for Accurate and Scalable Machine Learning Potentials](https://mlsanity.com/paper/2109.07421/) (2021)
- [Which Minimizer Does My Neural Network Converge To?](https://mlsanity.com/paper/2011.02408/) (2020)

## Built on by (most cited first, 9 of 9)

- [Evaluation of the MACE Force Field Architecture: from Medicinal Chemistry to Materials Science](https://mlsanity.com/paper/2305.14247/) (2023)
- [Uncertainty-biased molecular dynamics for learning uniformly accurate interatomic potentials](https://mlsanity.com/paper/2312.01416/) (2023)
- [Higher-Rank Irreducible Cartesian Tensors for Equivariant Message Passing](https://mlsanity.com/paper/2405.14253/) (2024)
- [Transfer learning for chemically accurate interatomic neural network potentials](https://mlsanity.com/paper/2212.03916/) (2022)
- [Physics-Informed Weakly Supervised Learning for Interatomic Potentials](https://mlsanity.com/paper/2408.05215/) (2024)
- [Breaking scaling relations with inverse catalysts: a machine learning exploration of trends in CO2 hydrogenation energy barriers](https://mlsanity.com/paper/2504.16493/) (2025)
- [Predicting Properties of Periodic Systems from Cluster Data: A Case Study of Liquid Water](https://mlsanity.com/paper/2312.01414/) (2023)
- [Thermally Averaged Magnetic Anisotropy Tensors via Machine Learning Based on Gaussian Moments](https://mlsanity.com/paper/2312.01415/) (2023)
- [Performance of universal machine-learned potentials with explicit long-range interactions in biomolecular simulations](https://mlsanity.com/paper/2508.10841/) (2025)

## Abstract (arXiv)

Artificial neural networks (NNs) are one of the most frequently used machine learning approaches to construct interatomic potentials and enable efficient large-scale atomistic simulations with almost ab initio accuracy. However, the simultaneous training of NNs on energies and forces, which are a prerequisite for, e.g., molecular dynamics simulations, can be demanding. In this work, we present an improved NN architecture based on the previous GM-NN model [V. Zaverkin and J. K"astner, J. Chem. Theory Comput. 16, 5410-5421 (2020)], which shows an improved prediction accuracy and considerably reduced training times. Moreover, we extend the applicability of Gaussian moment-based interatomic potentials to periodic systems and demonstrate the overall excellent transferability and robustness of the respective models. The fast training by the improved methodology is a pre-requisite for training-heavy workflows such as active learning or learning-on-the-fly.