18-762 Simulation and Optimization of Engineering Systems Through a Circuit Lens
12 units, Carnegie Mellon University
This course develops scalable numerical methods and optimization algorithms for engineering systems through a circuit-theoretic lens. It explores how numerical algorithms can be framed as physical systems, namely, as equivalent analog circuits, thereby recasting algorithm design as circuit design. This course explores successful industrial implementations of the equivalent circuit paradigm in circuits and power systems that leverage a physics-first lens to construct algorithms and open new opportunities in system design and control. The course draws on successful industrial implementations in circuits and power systems that use a physics-first approach to derive intuitive and scalable algorithms in system design and control. Students learn to combine engineering domain knowledge with numerical methods to exploit the structure and nonlinearities of mathematical problems arising in engineering systems. Applications include power grids, analog circuits, and state-space machine learning models. The course covers numerical methods for steady-state and frequency-domain analysis, followed by time-domain analysis, where students construct circuit-equivalent representations of dynamic systems and reinterpret numerical integration in terms of physical quantities such as charge and energy. The final portion extends these ideas to circuit-theoretic optimization in both steady-state and time-domain settings, including applications such as state estimation and optimal power flow. Students will be able to leverage the connection between numerical algorithms and circuit representations to design, analyze, and adapt methods for simulating and optimizing engineering systems, with emphasis on stability, efficiency, and scalability. The main deliverables for this course includes three projects aligned with the major sections of the course.
Prerequisites: 18-202 (min C) or 18-372 (min C) or 18-220 (min C)
Offered: Fall 2026
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