###### Abstract  
The phases of high-entropy alloys (HEAs) are crucial to their material properties. Although meta-learning can recommend a desirable algorithm for materials designers, it does not utilize the optimal solution information of similar historical problems in the HEA field. To address this issue, a transferable meta-learning model (MTL-AMWO) based on an adaptive migration walrus optimizer is proposed to predict the phases of HEAs. Firstly, a transferable meta-learning algorithm frame is proposed, which consists of meta-learning based on adaptive migration walrus optimizer, balanced-relative density peaks clustering, and transfer strategy. Secondly, an adaptive migration walrus optimizer model is proposed, which adaptively migrates walruses according to the changes in the average fitness value of the population over multiple iterations. Thirdly, balanced-relative density peaks clustering is proposed to cluster the samples in the source and target domains into several clusters with similar distributions, respectively. Finally, the transfer strategy adopts the maximum mean discrepancy to find the most matching historical problem and transfer its optimal solution information to the target domain. The effectiveness of MTL-AMWO is validated on 986 samples from six datasets, including 323 quinary HEAs, 366 senary HEAs, and 297 septenary HEAs. The experimental results show that the MTL-AMWO achieves better performance than other algorithms. high-entropy alloys; phase prediction; walrus optimizer; density peaks clustering; transfer learning +
Footnote †: journal: applied sciences  
0000-0001-9977-3389-3399-3/2000/00000-0000-0000-0000-0000-0000-00000-0000-00000-00000-00000-00000-00000-00000-00000-00000-00000-00000-000000-000000-000000-0000000-000000-0000000-0000000-00000000-0000000000000000 theory (DFT) and first principles are other approaches to predict the phases of HEAs, both are computationally intensive and inefficient [14; 15]. The parametric method, which is another approach to predict the phases of HEAs, can effectively reduce the computational burden [5]. However, its heavy reliance on empirical knowledge limits its application scope. In recent years, machine-learning (ML) has been increasingly applied to the field of materials due to its high efficiency and powerful learning ability [16; 17]. Although ML has been applied to predict the phases of HEAs and achieved promising results, the accuracies among different ML algorithms based on the same dataset can be significantly different [18]. Recommending an ideal algorithm for the materials designers can significantly reduce their workload and shorten the materials development cycle. Meta-learning can recommend a suitable algorithm for materials designers. [PERSON] et al. [19] developed a novel approach to selecting the best-performing clustering algorithm by extracting meta-knowledge from datasets. [PERSON] et al. [20] proposed a dynamic ensemble pruning selection model by meta-learning to recommend the most competent ensemble pruning algorithm for a test sample. [PERSON] et al. [21] proposed a classification algorithm recommendation framework based on meta-learning and achieved promising results. In the field of HEAs, some scholars have conducted relevant research on meta-learning. [PERSON] et al. [22] proposed a method based on meta-learning recommendation, which can recommend algorithms with ideal accuracy to materials designers on some datasets. In the above studies, although ideal results were achieved by meta-learning, the optimization algorithms in meta-learning do not utilize the optimal solution set information of a similar historical problem. If the optimal solution set information of a similar historical problem can be transferred to the above meta-learning optimization algorithms, the performance of the model will be further improved. Transfer learning can employ the optimal solution set information of similar historical problems when solving a new problem, thereby improving the performance of the algorithm [23].