Short Course on Reduced Order Work Models

Prof. Matthias Heinkenschloss with the Department of Computational and Applied Mathematics, Rice University in Houston, Texas is offering a short course on Reduced Order Work Models at Trier University on behalf of the Research Training Group on Algorithmic Optimization. 

The following is an outline of the short course:

Many applications require the repeated solution of partial differential equations (PDEs) for different input parameters or even the solution of optimization problems governed by PDEs. These tasks can be computationally expensive, sometimes prohibitively expensive when carried out using only high fidelity PDE discretizations. Model order reduction systematically extracts key dynamics to generate low-order representations of the (high fidelity discretizations of the) PDEs so that quantities of interest generated from the PDE solutions are well approximated by these low-order representations.

This short course will introduce current methods for the computation of projection based reduced order models (ROMs), analyze the computational cost and the approximation properties of these ROMs, and demonstrate their application on model PDEs. The second part of this course will introduce approaches for the integration of projection based ROMs into the solution of some classes of PDE constrained optimization problems.

The course will consist of five lectures, with the tentative lecture schedule as follows:

1. PDE model problems and their discretizations; PDE constrained optimization model problems and their discretizations; gradient and Hessian computations.

2. The Reduced Basis method and Proper Orthogonal Decomposition.

3. The (Discrete) Empirical Interpolation Method ( (D)EIM ).

4. ROMs for linear-quadratic PDE constrained optimization problems.

5. Approaches and challenges for the use of ROMs in nonlinear PDE constrained optimization problems.

The short course on Reduced Order Work Models will take place beginning on Tuesday, June 21, 2016 through Thursday, June 30, 2016.

For more information on the exact times and lecture hall, contact the organizer.