Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces

# ~~~
# This file is part of the paper:
#   
#           "Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces"
# by Michael Kartmann and Stefan Volkwein
# Preprint: https://arxiv.org/abs/2510.14479
#
# Copyright 2025 all developers. All rights reserved.
# License: Licensed as BSD 2-Clause License (http://opensource.org/licenses/BSD-2-Clause)
# Authors: Michael Kartmann
# 
# ~~~

In this repository, we provide the code for the numerical experiments of the paper "Optimality-Based Control Space Reduction for Infinite-Dimensional Control Spaces" by Michael Kartmann and Stefan Volkwein. A preprint is available here.

Citation

If you are using the code, please consider citing via

M. Kartmann, S Volkwein
Code for ”Optimality-Based Control Reduction for Infinite-Dimensional Control Spaces” (2025)
https://zenodo.org/records/17356821

Setup

To run the code you need to install the python package FEniCS 2019 in your (local) environment together with SciPy, NumPy and Matplotlib. This can be done using conda via

conda create -n control_reduction -c conda-forge python=3.9 fenics=2019.1.0 numpy scipy matplotlib

or using the provided environment.yml-file via

conda env create -f environment.yml

After installing all the packages, run one of the experiments, e.g. by

conda activate control_reduction
python main_rom_opti.py

Organization of the repository

The code consists of the main files

• main_rom_opti.py: the main file for the experiment in Section 5.3,
• main_adaptive_opti.py: the main file for the experiment in Section 5.4.

The modeling and discretization of the problem is realized in a PyMORish-way in the following files:

• discretizer.py: discretizes the problem to obtain a full-order model (FOM),
• model.py: contains the implementation of the full-order or reduced-order model (ROM),
• reductor.py: reduces the full-order model to obtain a reduced-order model,

Moreover, the following file contains the code for the adaptive optimization algorithm

• adaptive_opt.py: contains the implementation of adaptive POD optimization method (Algorithm 1).

Additionally there are some helper files.

Contact

If there are questions of any kind, don't hesitate to get in touch with us at michael.kartmann@uni-konstanz.de.