# Predicting the Effect of Processing Parameters on Caliber-Rolled Mg Alloys through Machine Learning
## 1 Introduction  
Multi-pass caliber rolling (MPCR) is a metal-forming process used to fabricate a rod-type product. A metallic material is inserted into a \"caliber\" between a pair of rolls, by which it goes through redundant strains as well as shape change. Although the idea of MPCR was reported in the early 2000s [1], it gained significant attention because of the study of [PERSON] et al. [2] published in 2018. These authors compared the mechanical properties of Fe-0.4C-2 Si-1 Cr-1 Mo steels subjected to either the MPCR process or a conventional method. The MPCR-processed steel presented peculiar fracture behavior resembling that of bamboo, leading to 16-fold higher impact toughness compared with conventional steel. Such a remarkable improvement was attributed to ultrafine elongated grains and nano-sized carbides fabricated by the MPCR process. The mechanical improvement by the MPCR process has attracted a large amount of attention, leading to a number of related studies using not only steels [3; 4; 5; 6] but also nonferrous metals, such as Ti [7; 8; 9; 10], Nb [11], and Mg alloys [12; 13; 14; 15; 16; 17]. In addition, the MPCR process enables the continuous manufacturing of bulk product, while inducing either ultrafine elongated or ultrafine equiaxed grains. For example, the authors fabricated a 2 m long Mg rod with an ultrafine-grained structure using an optimized MPCR process [13]. These engineering advantages are a novelty of the MPCR process contrasted by severe plastic deformation processes.  
A unique feature of the MPCR process is its strain distribution on the cross-sectional area, which varies with the type of calibers. The difference in local strain induces a heterogeneous grain structure and resultant variation in mechanical properties, particularly the Vickers microhardness [18; 19]. Despite its importance, no studies have attempted to predict the microhardness variation on the MPCR cross-section using a constitutive approach for two reasons. First, these approaches (e.g., the Hall-Petch equation [20; 21]) were made fora uniform grain structure, which mean they are inapplicable to the issue of interest. Second, the size of the microhardness database is smaller than that of other mechanical properties, such as flow curves, each including thousands of data points [22]. Accordingly, all related studies [18; 19; 23] used finite element analysis (FEA) to predict the microhardness variation in MPCR-processed alloys.  
Our research group has employed a machine-learning approach as an alternative resolution to predict the microhardness variation, because it is appropriate to solve a multi-variant nonlinear problem [24]. This approach has recently proven its usefulness for other types of process and material. [PERSON] et al. [25] developed a microhardness model for oxide precipitation hardened steel using machine learning, which provided good productivity with an R\({}^{2}\) of 0.95. [PERSON] et al. [26] anticipated the microhardness values of Ni alloy subjected to ultrasonic nanocrystalline surface modification depending on the chemical composition and processing parameter. Their machine-learning model yielded an R\({}^{2}\) of 0.98 from 37 testing datasets. However, it should be noted that such an approach has not been verified for either MPCR or Mg alloys. Therefore, this study aimed to predict the microhardness variation in MPCR-processed AZ31 Mg alloy depending on the position as well as the processing parameter. A predictive model were constructed using an artificial neural network (ANN), one of the most frequently used machine-learning approaches, with hyperparameter optimization. Furthermore, generative adversarial networks (GANs) were validated to confirm if it could resolve the issue of a small database.