The design of engineering systems – from chemical plants to molecular design – must be as effective as possible within limits imposed by costs, resources, physical laws, and safety rules. To find the best solution, engineers use computer programs called optimization solvers. Solvers rely on complex algorithms that need careful tuning by experts to perform well. This project will create a framework to better understand how these solvers work, focusing on how they rule out poor solutions and move toward the best one. By analyzing large amounts of data generated by the solvers and applying machine learning methods, the project will identify patterns to explain solver behavior. The results will help engineers interpret solver decisions and enable solvers to automatically improve their own performance, becoming faster and more accurate without manual adjustment. This data-driven approach can strengthen industrial automation systems, support materials and drug design, and speed up the development of new processes and products. In addition, the project will support education by building data science and computational skills in chemical engineering courses and by encouraging younger students to explore careers in STEM. This project adopts a novel dynamical-systems perspective to represent, learn, and optimize global optimization algorithms. In this framework, optimization algorithms are modeled as dynamical systems whose states evolve in function spaces defined over the feasible domain, with their evolution governed by linear operators acting on these spaces. This representation enables a unified and principled analysis of diverse global optimization methods. Specifically, the dynamics of widely used global optimization algorithms in process systems engineering and machine learning—such as stochastic gradient Langevin dynamics, branch-and-bound, outer approximation, and black-box Bayesian optimization—will be learned directly from solver snapshot data or historical ex