Direct and surrogate optimization in applied superconductivity: state of the art, perspectives and challenges

Abstract In contemporary research and development, the high cost of superconducting materials and the growing demand for enhanced performance compel scientists and engineers to go beyond conventional problem-solving approaches, adopting more innovative and integrated design and operational strategies. This necessitates the identification of optimal solutions, typically involving the optimization of multiple objectives while adhering to predefined design constraints. Along the years, different methods, both analytical and numerical, have been proposed to solve specific classes of optimization problems, as more rigorous alternatives to tentative trial-and-error approaches. In real-world superconducting problems , direct optimization faces two significant drawbacks: the large number of objective/constraint evaluations typically required to thoroughly explore the design domain, and the time-intensive numerical calculations involved in simulating complex physical phenomena. Consequently, beyond developing more computationally efficient direct optimization algorithms, machine learning and other techniques have been integrated into surrogate optimization approaches to enable the solution of otherwise computationally intractable problems. In this article, a topical review is presented to describe the state of the art of direct and surrogate optimization used to optimize superconducting devices.