This thesis investigates the optimization of Josephson junction (JJ) based memorydevices integrated with magnetic tunnel junctions (MTJs) for cryogenic computing applications, as part of the NSF-funded DISCoVER Expedition. The study leverages COMSOL Multiphysics simulations to model the electromagnetic behavior of JJ-MTJ hybrid structures, focusing on the modulation of the superconducting critical current (Ic) by the MTJ's fringe magnetic fields. The simulations, grounded in Ginzburg-Landau theory, capture key phenomena such as Abrikosov vortex formation and Fraunhofer pattern shifts, enabling the identification of distinct memory states basedon parallel and antiparallel MTJ magnetization configurations. To enhance device performance, Gaussian Process Regression (GPR) and Bayesian Optimization are employed to explore the design space, optimizing parameters such as MTJ geometry and material properties. Two datasets are developed: one varying permalloy magnetization and thickness, and another incorporating the full MTJ structure to quantify the memory window (ΔIc). The results demonstrate robust GPR predictions with low uncertainty, validating the approach for ML-driven design. Additionally, the thesis includes insights from a part-time internship at Soctera Inc., where nanofabrication techniques, including CVD silicon nitride deposition and ICP etching, were explored to improve GaN-based HEMT performance. This work establishes a scalable framework for physics-based simulation and machine learning- assisted optimization of superconducting memory devices, contributing to the development of energy-efficient, post-CMOS computing technologies.