ROM: Reduced Order Modelling

Trond Kvamsdal

This course introduces the theory, algorithms, and applications of reduced order modeling for large-scale statical and dynamical systems governed by differential equations. Students will learn both (lightly) intrusive (projection-based) and non-intrusive (data-driven) ROM techniques, with applications in structural/solid mechanics, fluid mechanics, control, and uncertainty quantification. Special emphasis will be given to applications relevant to offshore wind energy.

After completing this course, students will have acquired a solid theoretical and practical understanding of reduced order modelling techniques for large-scale systems governed by differential equations. They will learn how to construct efficient reduced models from high-fidelity simulations using methods such as Proper Orthogonal Decomposition (POD), Galerkin projection, and Reduced Basis methods. The course will also introduce hyper-reduction techniques for nonlinear systems and data-driven approaches to model reduction.

Students will develop the ability to analyse the accuracy, stability, and computational efficiency of reduced models and to implement ROM algorithms in practical computational frameworks. Through examples from fluid mechanics, solid mechanics, and multiphysics systems, participants will gain insight into how reduced order models can be used to accelerate simulation, enable real-time prediction, and support tasks such as optimization, control, and uncertainty quantification in modern computational engineering.

Digital lectures (made available as video recordings after the lectures) presenting theory and illustrative examples. Exercises are given but are not mandatory. Lectures, all written documentation and the exam are given in English. Students are free to choose Norwegian or English for written assessments including the exam.

Home examination that require the use of digital aids through the use of the INSPERA system. Weighted 100 out of 100. Permitted examination aids A: All printed and hand-written support material is allowed. All calculators are allowed. Retake of examination may be given as an oral examination. The retake exam is in August.

The courses TMA4215 Numerical Mathematics and TMA4212 Numerical Solution of Differential Equations by Difference Methods, TMA4220 Numerical Solution of Partial Differential Equations Using Element Methods, or equivalent.

Bachelor's/Master's in science or technology.

Will be announced at the start of the course.