Random Feature Hamiltonian Networks for N-Body Problems

Bachelor's Thesis: RF-HNNs-Thesis.pdf
Bachelor's Thesis Presentation: RF-HNNs-Presentation.pdf

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Original Work

This repository is based on the implementation from: Training Hamiltonian Neural Networks without Backpropagation

• Repository: https://github.com/AlphaGergedan/Sampling-HNNs
  
• Paper: https://arxiv.org/abs/2411.17511

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Models

The following models are available:

• MLP: ODE-Net, directly approximates q_dot and p_dot. paper

• HNN: Hamiltonian neural network approximates H, then recovers q_dot and p_dot using automatic differentiation and Hamilton’s equations. paper

All models are available in sampled form (S-MLP, S-HNN). In sampled models, hidden-layer parameters are randomly sampled and the final layer is computed using a least-squares solution.
Different sampling strategies are available through the SWIM method. paper

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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 the original paper.

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This Project

This repository extends the original Sampled-HNN framework to gravitational N-body systems.

Main additions:

• 2-body orbit generation : src/data/two_body_orbit_generator.py
• 3-body orbit generation : src/data/three_body_orbit_generator.py
• Hamiltonian formulation of the 2-body system : src/hamiltonian/two_body.py
• Hamiltonian formulation of the 3-body system : src/hamiltonian/three_body.py
• Symplectic integrators : src/integrators/
• Training and evaluation notebooks for 2-body and 3-body systems : analyze_two_body.ipynb & analyze_three_body.ipynb
• Generated plots for the thesis plots/