System Norm Regularization Methods for Koopman Operator Approximation

This repository contains the companion code for System Norm Regularization Methods for Koopman Operator Approximation. All the code required to generate the paper's plots from raw data is included here.

The regression methods detailed in the paper are implemented in pykoop, the authors' Koopman operator identification library. This repository simply includes the appropriate calls to pykoop to reproduce the paper's results.

This software relies on doit to automate plot generation and hydra to automate experiment execution.

Requirements

This software is compatible with Linux, macOS, and Windows. It was developed on Arch Linux with Python 3.10.1, while the experiments used in the corresponding paper were run on Windows 10 with Python 3.9.2. The pykoop library supports any version of Python above 3.7.12. You can install Python from your package manager or from the official website.

SciPy 1.7.3 was used to generate the paper results, but SciPy 1.11.1 is specified in requirements.txt due to a security alert.

The performance statistics presented are from the MOSEK solver running with 16 threads on a PC with an Intel Core i7-10700K processor and 64 GiB of RAM.

Warning: You probably cannot run this code on your laptop. The experiments using the soft robot dataset are particularly demanding. A desktop with at least 16 GiB of RAM is recommended.

Installation

To clone the repository and its submodule, which contains the soft robot dataset, run

$ git clone --recurse-submodules [email protected]:decarsg/system_norm_koopman.git

The recommended way to use Python is through a virtual environment. Create a virtual environment (in this example, named venv) using

$ python -m virtualenv venv

Activate the virtual environment with¹

$ source ./venv/bin/activate

To use a specific version of Python in the virtual environment, instead use

$ source ./venv/bin/activate --python <PATH_TO_PYTHON_BINARY>

If the virtual environment is active, its name will appear at the beginning of your terminal prompt in parentheses:

(venv) $ 

To install the required dependencies in the virtual environment, including pykoop, run

(venv) $ pip install -r ./requirements.txt

The LMI solver used, MOSEK, requires a license to use. You can request personal academic license here. You will be emailed a license file which must be placed in ~/mosek/mosek.lic².

Usage

To automatically generate all the plots used in the paper, run

(venv) $ doit

in the repository root. This command will:

1. Preprocess the datasets in datasets/ and place the outputs in build/datasets/
2. Run the necessary experiments using the datasets and place the outputs in build/hydra_outputs/
3. Profile the code and and place the results in build/mprof_outputs/
4. Generate the plots and place the results in build/figures/

This process can take upwards of 8 hours. It requires at least 16 GiB of RAM. You can optionally add -v2 to the command to print more detailed information about the process as it runs

To execute just one task and its dependencies, run

(venv) $ doit <TASK_NAME>

To see a list of all available task names, run

(venv) $ doit list --all

For example, to generate only the FASTER eigenvalue plot, run

(venv) $ doit plot:faster_eig

The required experiments will be run automatically by doit. The experiment:* and profile:* tasks used in the paper are:

Task name	Execution time (hh:mm:ss)
experiment:faster__polynomial2__edmd	00:00:06
experiment:faster__polynomial2__srconst_099	00:00:39
experiment:faster__polynomial2__srconst_1	00:00:07
experiment:soft_robot__polynomial3_delay1__edmd	00:00:22
experiment:soft_robot__polynomial3_delay1__hinf	02:27:41
experiment:soft_robot__polynomial3_delay1__hinf_dmdc	00:23:41
experiment:soft_robot__polynomial3_delay1__hinfw	04:00:20
experiment:soft_robot__polynomial3_delay1__srconst_0999	00:25:50
experiment:soft_robot__polynomial3_delay1__srconst_0999_dmdc	00:05:27
profile:hinf	00:15:09
profile:hinf_dmdc	00:03:01
profile:srconst_0999	00:08:52
profile:srconst_0999_dmdc	00:02:03

Other experiments are listed by doit list --all, but they are not used.

If you have a pre-built copy of build/hydra_outputs/ or other build products, doit will think they are out-of-date and try to rebuild them. To prevent this, run

(venv) $ doit reset-dep

after placing the folders in the right locations. This will force doit to recognize the build products as up-to-date and prevent it from trying to re-generate them. This is useful when moving the build/ directory between machines.

Manually Calling Hydra

Hydra is responsible for running experiments from configuration files. Normally, it is called by doit. If you want to run your own experiment with this repository, you can manually call Hydra with (for example)

(venv) $ python ./run_experiment.py dataset=./build/datasets/faster.pickle \
> lifting_functions=polynomial2 regressor=hinf

Where polynomial2 and hinf correspond to yaml files in config/lifting_functions/ and config/regressor/ respectively. You can also override yaml settings in the command line:

(venv) $ python ./run_experiment.py dataset=./build/datasets/faster.pickle \
> lifting_functions=polynomial2 regressor=hinf regressor.regressor.alpha=1

The Hydra outputs will appear in outputs/<DATE>/<TIME>/.

Repository Layout

The files and folders of the repository are described here:

Path	Description
build/	Contains all doit outputs, including plots.
config/	Contains configuration files for running experiments with Hydra.
datasets/	Contains raw datasets and their documentation.
dodo.py	Describes all of doit's behaviour, like a Makefile. Also contains plotting code.
run_experiment.py	Script used by Hydra to run experiments from configuration files.
requirements.txt	Contains required Python packages with versions.
LICENSE	Repository license.
README.md	This file!

If you want to know implementation details about the regressors presented in the paper, look at the pykoop repository. If you're interested in the specific parameters these regressors were called with, check out the yaml files in config/. Post-processing calculations are done in run_experiment.py, while plotting code can be found in dodo.py.

Footnotes

1. On Windows, use > \venv\Scripts\activate. ↩

2. On Windows, place the license in C:\Users\<USER>\mosek\mosek.lic. ↩