# Symmetry- and Property-Aware Crystal Generation with Reinforcement Learning for Inverse Materials Design

arXiv: https://arxiv.org/abs/2609.13468 · HTML: https://mlsanity.com/paper/2609.13468/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 55 references that are in the map.
- First posted on arXiv 11 Sep 2026.

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

- [Classifier-Free Diffusion Guidance](https://mlsanity.com/paper/2207.12598/) (2022)
- [Training Diffusion Models with Reinforcement Learning](https://mlsanity.com/paper/2305.13301/) (2023)
- [DPOK: Reinforcement Learning for Fine-tuning Text-to-Image Diffusion Models](https://mlsanity.com/paper/2305.16381/) (2023)
- [Crystal Diffusion Variational Autoencoder for Periodic Material Generation](https://mlsanity.com/paper/2110.06197/) (2021)
- [Crystal Structure Prediction by Joint Equivariant Diffusion](https://mlsanity.com/paper/2309.04475/) (2023)
- [Space Group Constrained Crystal Generation](https://mlsanity.com/paper/2402.03992/) (2024)
- [SymmCD: Symmetry-Preserving Crystal Generation with Diffusion Models](https://mlsanity.com/paper/2502.03638/) (2025)
- [Guiding Generative Models to Uncover Diverse and Novel Crystals via Reinforcement Learning](https://mlsanity.com/paper/2511.07158/) (2025)
- [Reinforcement Fine-Tuning for Materials Design](https://mlsanity.com/paper/2504.02367/) (2025)
- [Ab Initio Structure Solutions from Nanocrystalline Powder Diffraction Data](https://mlsanity.com/paper/2406.10796/) (2024)
- [CrystalGym: A New Benchmark for Materials Discovery Using Reinforcement Learning](https://mlsanity.com/paper/2509.23156/) (2025)

## Built on by (most cited first, 1 of 1)

- [Reinforcement Learning on the Discrete Composition Channel of a Crystal Generator: Validated Gains and Reward Hacking](https://mlsanity.com/paper/2610.03880/) (2026)

## Abstract (arXiv)

The inverse design of crystalline materials ultimately seeks structures with desired physical properties. However, for many functional responses, a favorable numerical value is meaningful only when supported by the symmetry of the underlying crystal. Without the appropriate crystallographic constraints, an apparent response may be ill defined, accidental, or not symmetry protected. Here we introduce SPARC, a symmetry- and property-aware reinforcement learning framework that optimizes physical objectives while preserving the structural conditions required for their realization. We demonstrate SPARC on two complementary tasks. The first targets strong uniaxial dielectric anisotropy, a tensorial response that is well defined only within appropriate crystal classes. The second maximizes the spectroscopic limited maximum efficiency, a scalar device-level objective without a prescribed symmetry class, allowing the framework to identify favorable crystallographic motifs. These results show that symmetry is not merely an additional design constraint, but a physical foundation for generating candidates with meaningful, robust, and realizable functional properties.