Training Hamiltonian neural networks without backpropagation

Source code for our paper on approximating Hamiltonian with sampled neural networks

Models

Available models are:

• MLP: ODE-Net, directly approximates q_dot and p_dot. paper
• HNN: Hamiltonian neural network approximates H, then q_dot and p_dot are recovered using automatic differentiation and Hamilton's equations. paper

All the models are available in sampled form. Sampled models have the S- prefix, which stands for Sampled. In this case, the model's hidden layer parameters are sampled, and the network's last layer is set using the least-squares solution. Different sampling options and resampling using approximate values are available for the SWIM method. paper

Here are the sampled ODE-Net (S-MLP) and HNN (S-MLP) models with their architecture illustrations for comparison:

---

Setup

Submodule

This project depends on the submodule swimnetworks:

git submodule init
git submodule update

to clone the submodule.

Environment

Create the conda environment:

conda env create --file=environments.yml

Then activate it with conda activate s-hnn.

Examples

After setting up the conda environment, you can use the bash script main located at the root of the project.

• Run ./main --help for usage.
• Training a traditional network: ./main --target single_pendulum --model {MLP,HNN}
• Sampling a network: ./main --target single_pendulum --model {S-MLP,S-HNN}

Here is an example to quickly train a Sampled-HNN for single pendulum:

python src/main.py --target single_pendulum --model S-HNN

First-order error correction example:

python src/main_limited_data.py --target single_pendulum --model S-HNN

For details you can refer to our paper paper.

---

Paper experiments

• All the experiment results listed in our paper, including all the trained models, are stored under /experiments as pickle files and categorized.
• In order to reproduce the experiments, refer to the scripts /src/*experiment.py.
• In order to analyze the results we prepared notebooks located at the root of the project /analyze-*.ipynb.
• The scripts /batch*.sh are used to conduct the experiments listed in our paper in a cluster environment.
• The notebook error_correction_demonstration.ipynb contains error correction experiments.

---

Citation

If you use Sampled-HNNs in your research, please cite our paper.