# Grain Knowledge Graph Representation Learning: A New Paradigm for Microstructure-Property Prediction

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Dataset

#### 2.1.1. Polycrystal Sample Preparation

#### 2.1.2. Dataset Preparation

#### 2.2. Representation of the Grain Knowledge Graph

#### 2.2.1. Node Representation

#### 2.2.2. Edge Representation

#### 2.2.3. Representation Structure Analysis

#### 2.3. Grain Knowledge Graph Representation Calculation

#### 2.3.1. Overview of the HGGAT

#### 2.3.2. The Propagation Process of HGGAT

## 3. Results

#### 3.1. Experiment Settings

#### 3.2. Prediction Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Grain knowledge graph. Each node in the figure represents a crystal grain in the microstructure, and the edges between nodes represent the grain boundaries between the original crystal grains.

**Figure 2.**Grain node construction process. Each grain in the IPF map corresponds to each grain node in the graph. Each node stores the features of the grain.

**Figure 3.**Grain size discretization and size attribute node construction. $Siz{e}_{max}$ ($Siz{e}_{min}$) denotes the largest-scale grain size (the smallest-scale grain size). According to the interval length ${c}_{s}$, the grains are divided into each interval. There are ${N}_{s}$ intervals in total, ${N}_{s}=\lceil (Siz{e}_{max}-Siz{e}_{min})/{c}_{s}\rceil $. For each interval, the corresponding node on the left is constructed.

**Figure 4.**Grain orientation discretization and orientation attribute node construction. (

**a**) Simulated Euler angle data distribution. Each orientation is determined by three Euler points. (

**b**) The three-dimensional orientation space is discretized, and each orientation point can be divided into a discrete three-dimensional space. (

**c**) For each discrete three-dimensional space, the corresponding orientation attribute node is constructed.

**Figure 5.**Grain-grain edge construction. According to the connection relationship of the crystal grains (i.e., the grain boundary), the edges between the grain nodes are constructed.

**Figure 6.**Grain-size edge construction. First, the corresponding size categories of grains are calculated, and then, the corresponding size category nodes (size attribute nodes) are connected to the grain nodes. In this way, the grain node and the corresponding size attribute node constitute a subordination relationship.

**Figure 7.**Grain-orientation edge construction. First, the grains are classified into corresponding orientation categories, and then, the corresponding orientation category nodes (orientation attribute nodes) are connected to the grain nodes. In this way, the grain node and the orientation attribute node constitute a subordination relationship.

**Figure 8.**Representation structure comparison. (

**a**) The image storage structure. (

**b**) The grain knowledge graph storage structure.

**Figure 10.**Fitting result. “ Ultimate Tensile Strength” means that UTS is used as the label during training and testing; “Elongation” means that EL is used as the label during training and testing; “Yield Strength” means that YS is used as the label during training and testing; “All” means that UTS, EL, and YS are used together as the label of the data in the experiment, i.e., multi-label learning and prediction task.

Alloy | Mg | Zn | Li | Al |
---|---|---|---|---|

Mg-2Zn | Bal | 1.99 | - | - |

Mg-2Zn-1Li | Bal | 1.67 | 1.11 | - |

Mg-2Zn-3Li | Bal | 1.82 | 3.08 | - |

Mg-2Zn-1Gd | Bal | 1.74 | 0.97 | - |

AZ31 | Bal | 2.98 | - | 0.99 |

**Table 2.**Multi-label learning model performance of yield strength (YS), ultimate tensile strength (UTS), and elongation (EL). ↑(↓) means that, the higher (lower), the better (worse).

Model | MSE ↓ | MAE ↓ | EV ↑ | ${\mathbf{R}}^{2}$↑ |
---|---|---|---|---|

Ridge | 0.139 | 0.299 | 0.850 | 0.836 |

SVR | 0.176 | 0.351 | 0.796 | 0.792 |

KNN | 0.160 | 0.336 | 0.834 | 0.810 |

RF | 0.157 | 0.250 | 0.841 | 0.802 |

MLP | 0.153 | 0.305 | 0.844 | 0.819 |

GGAT | 0.116 | 0.234 | 0.873 | 0.865 |

HGGAT(Our) | 0.051 | 0.164 | 0.943 | 0.941 |

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## Share and Cite

**MDPI and ACS Style**

Shu, C.; He, J.; Xue, G.; Xie, C.
Grain Knowledge Graph Representation Learning: A New Paradigm for Microstructure-Property Prediction. *Crystals* **2022**, *12*, 280.
https://doi.org/10.3390/cryst12020280

**AMA Style**

Shu C, He J, Xue G, Xie C.
Grain Knowledge Graph Representation Learning: A New Paradigm for Microstructure-Property Prediction. *Crystals*. 2022; 12(2):280.
https://doi.org/10.3390/cryst12020280

**Chicago/Turabian Style**

Shu, Chao, Junjie He, Guangjie Xue, and Cheng Xie.
2022. "Grain Knowledge Graph Representation Learning: A New Paradigm for Microstructure-Property Prediction" *Crystals* 12, no. 2: 280.
https://doi.org/10.3390/cryst12020280