# Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction

arXiv: https://arxiv.org/abs/2306.10045 · HTML: https://mlsanity.com/paper/2306.10045/

## Key facts

- Cited by 37 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 84 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Builds on (most cited first, 30 of 30)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Recipe for a General, Powerful, Scalable Graph Transformer](https://mlsanity.com/paper/2205.12454/) (2022)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [Junction Tree Variational Autoencoder for Molecular Graph Generation](https://mlsanity.com/paper/1802.04364/) (2018)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [GemNet: Universal Directional Graph Neural Networks for Molecules](https://mlsanity.com/paper/2106.08903/) (2021)
- [OGB-LSC: A Large-Scale Challenge for Machine Learning on Graphs](https://mlsanity.com/paper/2103.09430/) (2021)
- [Do Transformers Really Perform Bad for Graph Representation?](https://mlsanity.com/paper/2106.05234/) (2021)
- [Learning from Protein Structure with Geometric Vector Perceptrons](https://mlsanity.com/paper/2009.01411/) (2020)
- [GraphAF: a Flow-based Autoregressive Model for Molecular Graph Generation](https://mlsanity.com/paper/2001.09382/) (2020)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [GraphDF: A Discrete Flow Model for Molecular Graph Generation](https://mlsanity.com/paper/2102.01189/) (2021)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Generating 3D Molecules for Target Protein Binding](https://mlsanity.com/paper/2204.09410/) (2022)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs](https://mlsanity.com/paper/2206.08515/) (2022)
- [Predicting materials properties without crystal structure: Deep representation learning from stoichiometry](https://mlsanity.com/paper/1910.00617/) (2019)
- [Learning Hierarchical Protein Representations via Complete 3D Graph Networks](https://mlsanity.com/paper/2207.12600/) (2022)
- [Advanced Graph and Sequence Neural Networks for Molecular Property Prediction and Drug Discovery](https://mlsanity.com/paper/2012.01981/) (2020)
- [Ewald-based Long-Range Message Passing for Molecular Graphs](https://mlsanity.com/paper/2303.04791/) (2023)
- [Topology-Aware Graph Pooling Networks](https://mlsanity.com/paper/2010.09834/) (2020)
- [Scalable deeper graph neural networks for high-performance materials property prediction](https://mlsanity.com/paper/2109.12283/) (2021)
- [Deep Learning of High-Order Interactions for Protein Interface Prediction](https://mlsanity.com/paper/2007.09334/) (2020)
- [IRNet: A General Purpose Deep Residual Regression Framework for Materials Discovery](https://mlsanity.com/paper/1907.03222/) (2019)

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

- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [Wyckoff Transformer: Generation of Symmetric Crystals](https://mlsanity.com/paper/2503.02407/) (2025)
- [QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules](https://mlsanity.com/paper/2306.09549/) (2023)
- [Towards Symmetry-Aware Generation of Periodic Materials](https://mlsanity.com/paper/2307.02707/) (2023)
- [Multimodal Foundation Models for Material Property Prediction and Discovery](https://mlsanity.com/paper/2312.00111/) (2023)
- [Equivariance via Minimal Frame Averaging for More Symmetries and Efficiency](https://mlsanity.com/paper/2406.07598/) (2024)
- [Crystalformer: Infinitely Connected Attention for Periodic Structure Encoding](https://mlsanity.com/paper/2403.11686/) (2024)
- [Invariant Tokenization of Crystalline Materials for Language Model Enabled Generation](https://mlsanity.com/paper/2503.00152/) (2025)
- [Neural P3M: A Long-Range Interaction Modeling Enhancer for Geometric GNNs](https://mlsanity.com/paper/2409.17622/) (2024)
- [Kinetic Langevin Diffusion for Crystalline Materials Generation](https://mlsanity.com/paper/2507.03602/) (2025)
- [M2Hub: Unlocking the Potential of Machine Learning for Materials Discovery](https://mlsanity.com/paper/2307.05378/) (2023)
- [A Space Group Symmetry Informed Network for O(3) Equivariant Crystal Tensor Prediction](https://mlsanity.com/paper/2406.12888/) (2024)
- [Siamese Foundation Models for Crystal Structure Prediction](https://mlsanity.com/paper/2503.10471/) (2025)
- [Materials Informatics Transformer: A Language Model for Interpretable Materials Properties Prediction](https://mlsanity.com/paper/2308.16259/) (2023)
- [Bridging Text and Crystal Structures: Literature-driven Contrastive Learning for Materials Science](https://mlsanity.com/paper/2501.12919/) (2025)
- [A Materials Foundation Model via Hybrid Invariant-Equivariant Architectures](https://mlsanity.com/paper/2503.05771/) (2025)
- [Beyond Structure: Invariant Crystal Property Prediction with Pseudo-Particle Ray Diffraction](https://mlsanity.com/paper/2509.21778/) (2025)
- [CrysAtom: Distributed Representation of Atoms for Crystal Property Prediction](https://mlsanity.com/paper/2409.04737/) (2024)
- [Predicting band gap from chemical composition: A simple learned model for a material property with atypical statistics](https://mlsanity.com/paper/2501.02932/) (2025)
- [CAST: Cross Attention based multimodal fusion of Structure and Text for materials property prediction](https://mlsanity.com/paper/2502.06836/) (2025)
- [PRISM: Periodic Representation with multIscale and Similarity graph Modelling for enhanced crystal structure property prediction](https://mlsanity.com/paper/2511.20362/) (2025)
- [PerCNet: Periodic Complete Representation for Crystal Graphs](https://mlsanity.com/paper/2312.14936/) (2023)
- [ADA-GNN: Atom-Distance-Angle Graph Neural Network for Crystal Material Property Prediction](https://mlsanity.com/paper/2401.11768/) (2024)
- [ReciNet: Reciprocal Space-Aware Long-Range Modeling for Crystalline Property Prediction](https://mlsanity.com/paper/2502.02748/) (2025)
- [GAGA: Gaussianity-Aware Gaussian Approximation for Efficient 3D Molecular Generation](https://mlsanity.com/paper/2507.09043/) (2025)
- [Benchmarking GNNs for OOD Materials Property Prediction with Uncertainty Quantification](https://mlsanity.com/paper/2511.11697/) (2025)
- [Machine Learning Multiscale Interactions](https://mlsanity.com/paper/2605.25710/) (2026)
- [Latent Diffusion Pretraining for Crystal Property Prediction](https://mlsanity.com/paper/2606.00776/) (2026)
- [Accelerating Material Property Prediction using Generically Complete Isometry Invariants](https://mlsanity.com/paper/2401.15089/) (2024)
- [PDDFormer: Pairwise Distance Distribution Graph Transformer for Crystal Material Property Prediction](https://mlsanity.com/paper/2408.12984/) (2024)

## Abstract (arXiv)

We study property prediction for crystal materials. A crystal structure consists of a minimal unit cell that is repeated infinitely in 3D space. How to accurately represent such repetitive structures in machine learning models remains unresolved. Current methods construct graphs by establishing edges only between nearby nodes, thereby failing to faithfully capture infinite repeating patterns and distant interatomic interactions. In this work, we propose several innovations to overcome these limitations. First, we propose to model physics-principled interatomic potentials directly instead of only using distances as in many existing methods. These potentials include the Coulomb potential, London dispersion potential, and Pauli repulsion potential. Second, we model the complete set of potentials among all atoms, instead of only between nearby atoms as in existing methods. This is enabled by our approximations of infinite potential summations, where we extend the Ewald summation for several potential series approximations with provable error bounds. Finally, we propose to incorporate our computations of complete interatomic potentials into message passing neural networks for representation learning. We perform experiments on the JARVIS and Materials Project benchmarks for evaluation. Results show that the use of interatomic potentials and complete interatomic potentials leads to consistent performance improvements with reasonable computational costs. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS/tree/main/OpenMat/PotNet).