# Automating Crystal-Structure Phase Mapping: Combining Deep Learning with Constraint Reasoning

arXiv: https://arxiv.org/abs/2108.09523 · HTML: https://mlsanity.com/paper/2108.09523/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 66 references that are in the map.
- First posted on arXiv 21 Aug 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Self-supervised Visual Feature Learning with Deep Neural Networks: A Survey](https://mlsanity.com/paper/1902.06162/) (2019)
- [GraphRNN: Generating Realistic Graphs with Deep Auto-regressive Models](https://mlsanity.com/paper/1802.08773/) (2018)
- [A Semantic Loss Function for Deep Learning with Symbolic Knowledge](https://mlsanity.com/paper/1711.11157/) (2017)
- [Neurosymbolic AI: The 3rd Wave](https://mlsanity.com/paper/2012.05876/) (2020)
- [EMNIST: an extension of MNIST to handwritten letters](https://mlsanity.com/paper/1702.05373/) (2017)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Deep Multi-Species Embedding](https://mlsanity.com/paper/1609.09353/) (2016)
- [End-to-End Learning for the Deep Multivariate Probit Model](https://mlsanity.com/paper/1803.08591/) (2018)
- [Materials Representation and Transfer Learning for Multi-Property Prediction](https://mlsanity.com/paper/2106.02225/) (2021)
- [Unsupervised Phase Mapping of X-ray Diffraction Data by Nonnegative Matrix Factorization Integrated with Custom Clustering](https://mlsanity.com/paper/1802.07307/) (2018)

## Built on by (most cited first, 9 of 9)

- [HeuriGym: An Agentic Benchmark for LLM-Crafted Heuristics in Combinatorial Optimization](https://mlsanity.com/paper/2506.07972/) (2025)
- [End-to-End Crystal Structure Prediction from Powder X-Ray Diffraction](https://mlsanity.com/paper/2401.03862/) (2024)
- [M2Hub: Unlocking the Potential of Machine Learning for Materials Discovery](https://mlsanity.com/paper/2307.05378/) (2023)
- [Probabilistic Phase Labeling and Lattice Refinement for Autonomous Material Research](https://mlsanity.com/paper/2308.07897/) (2023)
- [Real-time experiment-theory closed-loop interaction for autonomous materials science](https://mlsanity.com/paper/2410.17430/) (2024)
- [opXRD: Open Experimental Powder X-ray Diffraction Database](https://mlsanity.com/paper/2503.05577/) (2025)
- [Machine Learning Automated Approach for Enormous Synchrotron X-Ray Diffraction Data Interpretation](https://mlsanity.com/paper/2303.10881/) (2023)
- [Integrating Symbolic Reasoning into Neural Generative Models for Design Generation](https://mlsanity.com/paper/2310.09383/) (2023)
- [Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyond](https://mlsanity.com/paper/2506.14054/) (2025)

## Abstract (arXiv)

Crystal-structure phase mapping is a core, long-standing challenge in materials science that requires identifying crystal structures, or mixtures thereof, in synthesized materials. Materials science experts excel at solving simple systems but cannot solve complex systems, creating a major bottleneck in high-throughput materials discovery. Herein we show how to automate crystal-structure phase mapping. We formulate phase mapping as an unsupervised pattern demixing problem and describe how to solve it using Deep Reasoning Networks (DRNets). DRNets combine deep learning with constraint reasoning for incorporating scientific prior knowledge and consequently require only a modest amount of (unlabeled) data. DRNets compensate for the limited data by exploiting and magnifying the rich prior knowledge about the thermodynamic rules governing the mixtures of crystals with constraint reasoning seamlessly integrated into neural network optimization. DRNets are designed with an interpretable latent space for encoding prior-knowledge domain constraints and seamlessly integrate constraint reasoning into neural network optimization. DRNets surpass previous approaches on crystal-structure phase mapping, unraveling the Bi-Cu-V oxide phase diagram, and aiding the discovery of solar-fuels materials.