https://github.com/axect/neural_hamilton
Official implementation of the paper "Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?"
https://github.com/axect/neural_hamilton
classical-mechanics deep-learning hamiltonian-dynamics machine-learning neural-operator operator-learning
Last synced: 4 months ago
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Official implementation of the paper "Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?"
- Host: GitHub
- URL: https://github.com/axect/neural_hamilton
- Owner: Axect
- License: mit
- Created: 2024-09-09T02:33:20.000Z (8 months ago)
- Default Branch: main
- Last Pushed: 2025-01-10T01:14:44.000Z (4 months ago)
- Last Synced: 2025-01-22T21:17:52.660Z (4 months ago)
- Topics: classical-mechanics, deep-learning, hamiltonian-dynamics, machine-learning, neural-operator, operator-learning
- Language: Python
- Homepage: https://arxiv.org/abs/2410.20951
- Size: 146 KB
- Stars: 8
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# Neural Hamilton
[](https://arxiv.org/abs/2410.20951)
This repository contains the official implementation of the paper "Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?"
## Overview
Neural Hamilton reformulates Hamilton's equations as an operator learning problem, exploring whether artificial intelligence can grasp the principles of Hamiltonian mechanics without explicitly solving differential equations. The project introduces new neural network architectures specifically designed for operator learning in Hamiltonian systems.
Key features:
- Novel algorithm for generating physically plausible potential functions using Gaussian Random Fields and cubic B-splines
- Multiple neural network architectures (DeepONet, TraONet, VaRONet, MambONet) for solving Hamilton's equations
- Comparison with traditional numerical methods (RK4)
- Performance evaluation on various physical potentials (harmonic oscillators, double-well potentials, Morse potentials)
## Installation
### Prerequisites
- [Rust & Cargo](https://rustup.rs/)
- Python 3.8+
- CUDA (optional, for GPU support)
- [uv](https://github.com/astral-sh/uv) (recommended) or pip
### Setup
1. Clone the repository:
```bash
git clone https://github.com/Axect/Neural_Hamilton
cd Neural_Hamilton
```
2. Install the required packages:
```bash
# Use uv with sync requirements.txt (recommended)
uv pip sync requirements.txt
# Or use uv (fresh install)
uv pip install -U torch wandb survey polars numpy optuna matplotlib scienceplots beaupy rich
# Or use pip
pip install -r requirements.txt
```
## Usage
### Data Generation
To generate training & validation data with Rust:
```bash
cargo run --release --bin neural_hamilton
```
To generate physically relevant potentials:
```bash
cargo run --release --bin
```
For `potential_name`, there are six options:
- `sho`: Simple Harmonic Oscillator
- `quartic`: Double-well
- `morse`: Morse
- `mff`: Mirrored Free Fall
- `smff`: Softened Mirrored Free Fall
- `unbounded`: Unbounded potential example in the paper
### Training Models
The main training script can be run with different dataset sizes:
```bash
python main.py --data normal --run_config configs/run_config.yaml # 10,000 potentials
python main.py --data more --run_config configs/run_config.yaml # 100,000 potentials
python main.py --data much --run_config configs/run_config.yaml # 1,000,000 potentials
```
For hyperparameter optimization:
```bash
python main.py --data normal --run_config configs/run_config.yaml --optimize_config configs/optimize_config.yaml
```
### Analyzing Results
To analyze trained models:
```bash
python analyze.py
```
The script provides options to:
- Evaluate model performance on test datasets
- Generate visualizations of potential functions and trajectories
- Compare performance with RK4 numerical solutions
### Model Architectures
1. **DeepONet**: Baseline neural operator model (config example: `configs/deeponet_run.yaml`)
```yaml
net_config:
nodes: 128
layers: 3
branches: 10
```
2. **VaRONet**: Variational Recurrent Operator Network (config example: `configs/varonet_run.yaml`)
```yaml
net_config:
hidden_size: 512
num_layers: 4
latent_size: 30
dropout: 0.0
kl_weight: 0.1
```
3. **TraONet**: Transformer Operator Network (config example: `configs/traonet_run.yaml`)
```yaml
net_config:
d_model: 64
nhead: 8
num_layers: 3
dim_feedforward: 512
dropout: 0.0
```
4. **MambONet**: Mamba Operator Network (config example: `configs/mambonet_run.yaml`)
```yaml
net_config:
d_model: 128
num_layers1: 4
n_head: 4
num_layers2: 4
d_ff: 1024
```
## Key Results
1. Performance Comparison:
- MambONet consistently outperforms other architectures and RK4
- Models show improved performance with larger training datasets
- Neural approaches maintain accuracy over longer time periods compared to RK4
2. Computation Time:
- TraONet demonstrates fastest computation time
- MambONet and DeepONet show comparable speeds to RK4
- VaRONet requires more computational resources
3. Physical Potential Tests:
- Superior performance on Simple Harmonic Oscillator, Double Well, and Morse potentials
- Successful extrapolation to non-differentiable potentials (Mirrored Free Fall)
- Improved accuracy on smoothed variants (Softened Mirrored Free Fall)
## Citation
If you use this code in your research, please cite:
```bibtex
@misc{kim2024neuralhamiltonaiunderstand,
title={Neural Hamilton: Can A.I. Understand Hamiltonian Mechanics?},
author={Tae-Geun Kim and Seong Chan Park},
year={2024},
eprint={2410.20951},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2410.20951},
}
```
## License
[MIT License](LICENSE)
## Acknowledgments
This project uses code from the following repositories:
* [mamba.py](https://github.com/alxndrTL/mamba.py) - Implementation of Mamba and parallel scan used in MambONet
* [HyperbolicLR](https://github.com/Axect/HyperbolicLR) - Implementation of ExpHyperbolicLR scheduler