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This course offers a scientific machine learning (SciML) approach to the modeling, optimization, and control of dynamical systems. Students will learn to systematically integrate physics-based models and constraints into deep learning architectures, and to leverage data-driven methods for accelerating the solution of large-scale optimization and optimal control problems. Key topics include physics-informed neural networks, learning to optimize, neural differential equations, neural operators, and differentiable control. The course also examines real-world applications of these emerging SciML techniques in domains such as building energy management, networked dynamical systems, and power systems. Emphasis will be placed on practical, hands-on coding exercises and project-based assessments to reinforce theoretical concepts through implementation.