# Neural Structure Fields with Application to Crystal Structure Autoencoders

arXiv: https://arxiv.org/abs/2212.13120 · HTML: https://mlsanity.com/paper/2212.13120/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 53 references that are in the map.
- First posted on arXiv 8 Dec 2022.

## Builds on (most cited first, 11 of 11)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Predicting materials properties without crystal structure: Deep representation learning from stoichiometry](https://mlsanity.com/paper/1910.00617/) (2019)
- [Curriculum DeepSDF](https://mlsanity.com/paper/2003.08593/) (2020)
- [Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures](https://mlsanity.com/paper/1909.00949/) (2019)
- [Inverse design of two-dimensional materials with invertible neural networks](https://mlsanity.com/paper/2106.03013/) (2021)
- [A probabilistic deep learning approach to automate the interpretation of multi-phase diffraction spectra](https://mlsanity.com/paper/2103.16664/) (2021)

## Built on by (most cited first, 2 of 2)

- [Crystal-LSBO: Automated Design of De Novo Crystals with Latent Space Bayesian Optimization](https://mlsanity.com/paper/2405.17881/) (2024)
- [CrystalFramer: Rethinking the Role of Frames for SE(3)-Invariant Crystal Structure Modeling](https://mlsanity.com/paper/2503.02209/) (2025)

## Abstract (arXiv)

Representing crystal structures of materials to facilitate determining them via neural networks is crucial for enabling machine-learning applications involving crystal structure estimation. Among these applications, the inverse design of materials can contribute to explore materials with desired properties without relying on luck or serendipity. We propose neural structure fields (NeSF) as an accurate and practical approach for representing crystal structures using neural networks. Inspired by the concepts of vector fields in physics and implicit neural representations in computer vision, the proposed NeSF considers a crystal structure as a continuous field rather than as a discrete set of atoms. Unlike existing grid-based discretized spatial representations, the NeSF overcomes the tradeoff between spatial resolution and computational complexity and can represent any crystal structure. We propose an autoencoder of crystal structures that can recover various crystal structures, such as those of perovskite structure materials and cuprate superconductors. Extensive quantitative results demonstrate the superior performance of the NeSF compared with the existing grid-based approach.