# Towards End-to-End Structure Solutions from Information-Compromised Diffraction Data via Generative Deep Learning

arXiv: https://arxiv.org/abs/2312.15136 · HTML: https://mlsanity.com/paper/2312.15136/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 54 references that are in the map.
- First posted on arXiv 23 Dec 2023.

## Builds on (most cited first, 14 of 14)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Densely Connected Convolutional Networks](https://mlsanity.com/paper/1608.06993/) (2016)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Deep Speech 2: End-to-End Speech Recognition in English and Mandarin](https://mlsanity.com/paper/1512.02595/) (2015)
- [Data-Driven Approach to Encoding and Decoding 3-D Crystal Structures](https://mlsanity.com/paper/1909.00949/) (2019)
- [Identification of Crystal Symmetry from Noisy Diffraction Patterns by A Shape Analysis and Deep Learning](https://mlsanity.com/paper/2005.12476/) (2020)
- [CrysFormer: Protein Structure Prediction via 3d Patterson Maps and Partial Structure Attention](https://mlsanity.com/paper/2310.03899/) (2023)

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

- [Interpretable Multimodal Machine Learning Analysis of X-ray Absorption Near-Edge Spectra and Pair Distribution Functions](https://mlsanity.com/paper/2410.17467/) (2024)

## Abstract (arXiv)

The revolution in materials in the past century was built on a knowledge of the atomic arrangements and the structure-property relationship. The sine qua non for obtaining quantitative structural information is single crystal crystallography. However, increasingly we need to solve structures in cases where the information content in our input signal is significantly degraded, for example, due to orientational averaging of grains, finite size effects due to nanostructure, and mixed signals due to sample heterogeneity. Understanding the structure property relationships in such situations is, if anything, more important and insightful, yet we do not have robust approaches for accomplishing it. In principle, machine learning (ML) and deep learning (DL) are promising approaches since they augment information in the degraded input signal with prior knowledge learned from large databases of already known structures. Here we present a novel ML approach, a variational query-based multi-branch deep neural network that has the promise to be a robust but general tool to address this problem end-to-end. We demonstrate the approach on computed powder x-ray diffraction (PXRD), along with partial chemical composition information, as input. We choose as a structural representation a modified electron density we call the Cartesian mapped electron density (CMED), that straightforwardly allows our ML model to learn material structures across different chemistries, symmetries and crystal systems. When evaluated on theoretically simulated data for the cubic and trigonal crystal systems, the system achieves up to 93.4% average similarity with the ground truth on unseen materials, both with known and partially-known chemical composition information, showing great promise for successful structure solution even from degraded and incomplete input data.