Green's Function Analytic Continuation with VAE

This project implements a physics-informed machine learning framework for the analytic continuation of imaginary-time Green’s functions into real-frequency spectral functions. It is built around a Variational Autoencoder (VAE) that explicitly learns a pole-residue decomposition, providing a robust and interpretable reconstruction of spectral data from Quantum Monte Carlo (QMC) simulations.

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🔍 Overview

Analytic continuation is a notoriously ill-posed problem in many-body Condensed Matter Physics. Traditional approaches like Maximum Entropy can be unstable and sensitive to noise. This project tackles the problem by:

• Learning poles and residues directly via a VAE.
• Reconstructing spectral functions from noisy QMC Green's functions.
• Providing a flexible and extensible framework for physicists and researchers.

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🧠 Key Features

• ✅ Variational Autoencoder architecture
• ✅ Explicit pole and residue extraction from a learned distribution
• ✅ Supports synthetic and QMC Green's function imaginary-time inputs
• ✅ Modular code structure (training, evaluation, visualization)
• ✅ Easy to extend to other continuation tasks

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📁 Project Structure

greens-function-analytic-continuation/
├── README.md
├── LICENSE
├── requirements.txt
├── src/                                      # Main model and training code
│   ├── model.py                              # VAE class and architecture
│   ├── train.py                              # training and testing
│   ├── Green_reconstruction.py               # reconstructing poles and residues to Green's functions
│   ├── data_process.py                       # input data processing before feeding to network
├── synthetic-data/                           # Placeholder for input Green’s functions as sythetic data
│   ├── half-filled-gaussian                  # Green's functions corresponding to Gaussian spectral functions
│   ├── half-filled-lorentzian                # Green's functions corresponding to Lorentzian spectral functions
│   ├── Green_reconstruction.py               # reconstructing poles and residues to Green's functions
├── example-outputs/                          # Output poles, residues, plots
│   ├── out_gaussian_numpoles1_s1e-04_xi0.5-1 
│   ├── out_gaussian_numpoles1_s1e-04_xi0.5-1
├── examples/                                 # Example usage scripts
│   └── usage_example.py

⚙️ Installation

Clone the repository:

git clone https://github.com/george-issa/greens-function-analytic-continuation.git
cd greens-function-analytic-continuation

Install required packages:

pip install -r requirements.txt

Or with Conda:

conda env create -f environment.yml
conda activate gfvae

🚀 Usage

Train a model:

Execute the train file which will load the input data and train the model defined in model.py

python src/train.py

Visualize the results

Load the obtained poles and residues and plot the constructed spectral function using:

python example-outputs/spectral_poles_gaussian.py

📄 License

This project is licensed under the MIT License.

🙋 Contact

For questions, discussions, or collaborations, feel free to:

Open an issue

Submit a pull request

Connect on GitHub