Project structure

.
├── rahma_master_thesis.pdf # thesis pdf
├── plots                   # includes final plots used in the thesis
├── src                     # R-HNN implementation using swimnetworks module
│   ├── main.py             # main function for running and saving R-HNN experiments
│   ├── activations         # activation functions implementations
│   ├── error_functions     # error functions implementations
│   ├── hamiltonians        # Hamiltonian system implementations used
│   ├── integrators         # integrator implementations
│   ├── scripts             # scripts for creating plots from the saved experiments
│   ├── utils               # util functions
│   └── swimnetworks        # submodule used, see [here](https://github.com/AlphaGergedan/swimnetworks)
├── notebooks               # includes notebooks used for integration plots
│   └── integration
└── environments.yml

Setup

To create the required conda environment run: conda env create --file=environments.yml.

Run and Save Experiments

R-HNN implementation (Alg. 2) can be found in src/utils/swim.py inside hswim function. It is like a wrapper around the swimnetworks module (see original repo here) to be able to act like an HNN. For HNN reference see the papers by Greydanus et al., Bertalan et al..

For creating the scaling plots cluster provided by lrz is used. The batch files used to submit jobs can be found under src/scripts/batch-files.

The following examples are taken from the batch-files, note that the path to the main.py should be changed to the location of the main.py file, if you are in the project root of this repo and want to locally run, you should change it to src/main.py.

Single Pendulum

python src/main.py 'single_pendulum' -dof 1 -trainsetsize 1000 -qtrainlimstart -6.28 -qtrainlimend 6.28 -ptrainlimstart -6 -ptrainlimend 6 \
                                            -testsetsize 5000 -qtestlimstart -6.28 -qtestlimend 6.28 -ptestlimstart -6 -ptestlimend 6 \
                                     -repeat 100 -includebias -nhiddenlayers 1 -nneurons 200 -activation 'tanh' -parametersampler 'tanh' -rcond=1e-13 \
                                     -elmbiasstart=-6.28 -elmbiasend=6.28 -resampleduplicates \
                                     -trainrandomseedstart=3943 -testrandomseedstart=29548 -modelrandomseedstart=992472 \
                                     output_dir

Lotka-Volterra

python src/main.py 'lotka_volterra' -dof 1 -trainsetsize 4000 -qtrainlimstart -5 -qtrainlimend 5 -ptrainlimstart -5 -ptrainlimend 5 \
                                           -testsetsize 10000 -qtestlimstart -5  -qtestlimend 5 -ptestlimstart -5 -ptestlimend 5 \
                                    -repeat 100 -includebias -nhiddenlayers 1 -nneurons 1500 -activation 'tanh' -parametersampler 'tanh' -rcond=1e-13 \
                                    -elmbiasstart=-5 -elmbiasend=5 -resampleduplicates \
                                    -trainrandomseedstart=3943 -testrandomseedstart=29548 -modelrandomseedstart=992472 \
                                    output_dir

Double Pendulum

python src/main.py 'double_pendulum' -dof 2 -trainsetsize 20000 -qtrainlimstart -3.14 -3.14 -qtrainlimend 3.14 3.14 -ptrainlimstart -1 -1 -ptrainlimend 1 1 \
                                            -testsetsize 20000 -qtestlimstart -3.14 -3.14 -qtestlimend 3.14 3.14 -ptestlimstart -1 -1 -ptestlimend 1 1 \
                                            -repeat 10 -includebias -nhiddenlayers 1 -nneurons 1000 -activation 'tanh' -parametersampler 'tanh' -rcond=1e-13 \
                                            -elmbiasstart=-3.14 -elmbiasend=3.14 -resampleduplicates \
                                            -trainrandomseedstart=3943 -testrandomseedstart=29548 -modelrandomseedstart=992472 \
                                            output_dir

Henon-Heiles

python src/main.py 'henon_heiles_0.7_alpha' -dof 2 -trainsetsize 20000 -qtrainlimstart -1 -1 -qtrainlimend 1 1 -ptrainlimstart -1 -1 -ptrainlimend 1 1 \
                                                   -testsetsize 20000 -qtestlimstart -1 -1 -qtestlimend 1 1 -ptestlimstart -1 -1 -ptestlimend 1 1 \
                                                   -repeat 10 -includebias -nhiddenlayers 1 -nneurons 3000 -activation 'tanh' -parametersampler 'tanh' -rcond=1e-13 \
                                                   -elmbiasstart=-1 -elmbiasend=1 -resampleduplicates \
                                                   -trainrandomseedstart=3943 -testrandomseedstart=29548 -modelrandomseedstart=992472 \
                                                   output_dir

Figures

• All the scaling plots in the thesis can be created using the related script inside src/scripts/batch-files.
• For the integration plots (Fig. 3.11, Fig. 3.12, Fig. 3.14, Appendix Fig. 15-18, Appendix Fig. 20-23) for double pendulum and Henon-Heiles please refer to the notebooks under notebooks/integration. In order to create them locally you first need to run the experiment with the proper parameters. For the parameter values, please refer to the thesis.
• Fig. 3.15 can be created using the script src/scripts/run_finite_differences_experiment.sh, make sure to set the integrator to simulate the true flow to rk45 for the same plot.

Tip: Setting repeat too large can lead to longer runtimes, better reduce it to test locally. Also, make sure you set OMP_NUM_THREADS to the number of CPU cores of your node, in order utilize full capacity for numpy operations.

For any questions do not hesitate to contact me at: [email protected].