# Representations of molecules and materials for interpolation of quantum-mechanical simulations via machine learning

arXiv: https://arxiv.org/abs/2003.12081 · HTML: https://mlsanity.com/paper/2003.12081/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Mar 2020.

## Built on by (most cited first, 11 of 11)

- [Smooth, exact rotational symmetrization for deep learning on point clouds](https://mlsanity.com/paper/2305.19302/) (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)
- [Probing the effects of broken symmetries in machine learning](https://mlsanity.com/paper/2406.17747/) (2024)
- [Less can be more for predicting properties with large language models](https://mlsanity.com/paper/2406.17295/) (2024)
- [3DReact: Geometric deep learning for chemical reactions](https://mlsanity.com/paper/2312.08307/) (2023)
- [A Universal Framework for Featurization of Atomistic Systems](https://mlsanity.com/paper/2102.02390/) (2021)
- [Stress and heat flux via automatic differentiation](https://mlsanity.com/paper/2305.01401/) (2023)
- [Polyatomic Complexes: A topologically-informed learning representation for atomistic systems](https://mlsanity.com/paper/2409.15600/) (2024)
- [Evaluation of uncertainty estimations for Gaussian process regression based machine learning interatomic potentials](https://mlsanity.com/paper/2410.20398/) (2024)
- [Fast and Interpretable Machine Learning Modelling of Atmospheric Molecular Clusters](https://mlsanity.com/paper/2509.11728/) (2025)

## Abstract (arXiv)

Computational study of molecules and materials from first principles is a cornerstone of physics, chemistry, and materials science, but limited by the cost of accurate and precise simulations. In settings involving many simulations, machine learning can reduce these costs, often by orders of magnitude, by interpolating between reference simulations. This requires representations that describe any molecule or material and support interpolation. We comprehensively review and discuss current representations and relations between them, using a unified mathematical framework based on many-body functions, group averaging, and tensor products. For selected state-of-the-art representations, we compare energy predictions for organic molecules, binary alloys, and Al-Ga-In sesquioxides in numerical experiments controlled for data distribution, regression method, and hyper-parameter optimization.