Cooperative game during phase transformations in complex alloy systems

Phase-transformation models in high-entropy alloys face a dual challenge of scale and complexity because of their characteristics of complex systems. The phase-transformation theory in simple alloys is based on reductionism, which has limitations when used for complex systems. Under the framework of the renormalization group procedure, a machine-learning method was employed that can describe phase-transformations in alloy systems in a manner that differs from traditional data-driven machine learning. We have constructed a comprehensive alloy dataset, grounded in real experimental data, to validate our models. A 98 % accuracy rate has been achieved by the algorithm in the test set. Using the cooperative game theory to further explain the mathematical model established by machine learning, it is found that the established model can include some phase-transformation criteria found by previous researchers. The findings of this study provide insights into the order-disorder phase transformation in alloys from a new perspective, as well as some specific conclusions that are applicable to the design of complex alloys.