# Challenges in Non-Polymeric Crystal Structure Prediction: Why a Geometric, Permutation-Invariant Loss is Needed

arXiv: https://arxiv.org/abs/2509.00832 · HTML: https://mlsanity.com/paper/2509.00832/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 40 of its 79 references that are in the map.
- First posted on arXiv 31 Aug 2025.

## Builds on (most cited first, 30 of 40)

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- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Deep Closest Point: Learning Representations for Point Cloud Registration](https://mlsanity.com/paper/1905.03304/) (2019)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Flow Matching on General Geometries](https://mlsanity.com/paper/2302.03660/) (2023)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [GEOM: Energy-annotated molecular conformations for property prediction and molecular generation](https://mlsanity.com/paper/2006.05531/) (2020)
- [Geometric and Physical Quantities Improve E(3) Equivariant Message Passing](https://mlsanity.com/paper/2110.02905/) (2021)
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- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [FlowMM: Generating Materials with Riemannian Flow Matching](https://mlsanity.com/paper/2406.04713/) (2024)
- [3DRegNet: A Deep Neural Network for 3D Point Registration](https://mlsanity.com/paper/1904.01701/) (2019)
- [On the Expressive Power of Geometric Graph Neural Networks](https://mlsanity.com/paper/2301.09308/) (2023)
- [Periodic Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2209.11807/) (2022)
- [How To Train Your Deep Multi-Object Tracker](https://mlsanity.com/paper/1906.06618/) (2019)
- [A Hitchhiker's Guide to Geometric GNNs for 3D Atomic Systems](https://mlsanity.com/paper/2312.07511/) (2023)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Space Group Informed Transformer for Crystalline Materials Generation](https://mlsanity.com/paper/2403.15734/) (2024)
- [Efficient Approximations of Complete Interatomic Potentials for Crystal Property Prediction](https://mlsanity.com/paper/2306.10045/) (2023)

## Abstract (arXiv)

Crystalline structure prediction is an essential prerequisite for designing materials with targeted properties. Yet, it is still an open challenge in materials design and drug discovery. Despite recent advances in computational materials science, accurately predicting three-dimensional non-polymeric crystal structures remains elusive. In this work, we focus on the molecular assembly problem, where a set S of identical rigid molecules is packed to form a crystalline structure. Such a simplified formulation provides a useful approximation to the actual problem. However, while recent state-of-the-art methods have increasingly adopted sophisticated techniques, the underlying learning objective remains ill-posed. We propose a better formulation that introduces a loss function capturing key geometric molecular properties while ensuring permutation invariance over S. Remarkably, we demonstrate that within this framework, a simple regression model already outperforms prior approaches, including flow matching techniques, on the COD-Cluster17 benchmark, a curated non-polymeric subset of the Crystallography Open Database (COD).