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Operator Inference for Reduced Order Modeling

7 chapters · 33 lessons

1. 1. When Full Simulation Is Too Expensive

   4 lessons

   Identify problems where reduced order models add value and understand the tradeoffs between accuracy and speed.

2. 2. Proper Orthogonal Decomposition for Basis Extraction

   5 lessons

   Extract low-dimensional bases from snapshot data that capture dominant system behavior.

3. 3. Operator Inference for Dynamical Systems

   5 lessons

   Learn operators governing reduced dynamics from data while preserving structure.

4. 4. Validating Surrogate Model Reliability

   5 lessons

   Test surrogate models for accuracy, stability, and trustworthiness across parameter ranges.

5. 5. Parametric Reduced Order Models

   4 lessons

   Build surrogate models that adapt to varying parameters, geometries, and boundary conditions.

6. 6. Integration into Engineering Workflows

   5 lessons

   Deploy reduced order models for optimization, sensitivity analysis, and decision support.

7. 7. Case Studies Across Engineering Domains

   5 lessons

   Apply operator inference to fluid dynamics, structural mechanics, thermal systems, and energy applications.