*Article* **Standard Deviation Effect of Average Structure Descriptor on Grain Boundary Energy Prediction**

**Ruoqi Dang and Wenshan Yu \***

State Key Laboratory for Strength and Vibration of Mechanical Structures, Shaanxi Engineering Laboratory for Vibration Control of Aerospace Structures, School of Aerospace Engineering, Xi'an Jiaotong University, Xi'an 710049, China

**\*** Correspondence: wenshan@mail.xjtu.edu.cn

**Abstract:** The structural complexities of grain boundaries (GBs) result in their complicated property contributions to polycrystalline metals and alloys. In this study, we propose a GB structure descriptor by linearly combining the average two-point correlation function (PCF) and standard deviation of PCF via a weight parameter, to reveal the standard deviation effect of PCF on energy predictions of Cu, Al and Ni asymmetric tilt GBs (i.e., Σ3, Σ5, Σ9, Σ11, Σ13 and Σ17), using two machine learning (ML) methods; i.e., principal component analysis (PCA)-based linear regression and recurrent neural networks (RNN). It is found that the proposed structure descriptor is capable of improving GB energy prediction for both ML methods. This suggests the discriminatory power of average PCF for different GBs is lifted since the proposed descriptor contains the data dispersion information. Meanwhile, we also show that GB atom selection methods by which PCF is evaluated also affect predictions.

**Keywords:** grain boundary; descriptor; pair distribution function; grain boundary energy; machine learning method
