Projection-based model order reduction (PMOR) is an important pillar of physics-based machine learning. It is critical for computational-based design and optimization, statistical analysis, embedded computing, and real-time optimal control; and indispensable for scenarios where real-time, physics-based numerical simulation responses are desired. This course presents the basic mathematical theory for PMOR. Topics include: Orthogonal and oblique projections; Galerkin and Petrov-Galerkin projections; error analysis; proper orthogonal decomposition and connection with singular value decomposition; linear dynamical systems; balanced truncation methods; moment matching methods; nonlinear dynamical systems; local parametric database approaches; nonlinear approximation methods and connection with deep learning; the least-Squares Petrov Galerkin method; and hyperreduction. Course material is complemented by a balanced set of theoretical, algorithmic, and computer programming assignments. Prerequisites: CME 200 or equivalent, CME 263 or equivalent, and basic numerical methods for ODEs.
3 units · Letter or Credit/No Credit
Projection-based model order reduction (PMOR) is an important pillar of physics-based machine learning. It is critical for computational-based design and optimization, statistical analysis, embedded computing, and real-time optimal control; and indispensable for scenarios where real-time, physics-based numerical simulation responses are desired. This course presents the basic mathematical theory for PMOR. Topics include: Orthogonal and oblique projections; Galerkin and Petrov-Galerkin projections; error analysis; proper orthogonal decomposition and connection with singular value decomposition; linear dynamical systems; balanced truncation methods; moment matching methods; nonlinear dynamical systems; local parametric database approaches; nonlinear approximation methods and connection with deep learning; the least-Squares Petrov Galerkin method; and hyperreduction. Course material is complemented by a balanced set of theoretical, algorithmic, and computer programming assignments. Prerequisites: CME 200 or equivalent, CME 263 or equivalent, and basic numerical methods for ODEs.
Offered in Autumn 2026 at Stanford University.