PyTorch implement of the paper Neural Canonical Transformation with Symplectic Flows.

A symplectic normalizing flow learns slow and nonlinear collective modes in the latent space. The model reveals dynamical information from statistical correlations in the phase space.

Usage

0. Setup Guide

Both pytorch and numpy are required, you can install them using anaconda.

If you want to run the following demos, you need to download savings and datasets from Google Drive. To do this run:

python download_demo.py

1. Phase Space Density Estimation

1.1 Molecular Dynamics trajectory data

To train a neuralCT for molecular dynamics data, use density_estimation_md.py

python ./density_estimation_md.py -batch 200 -epoch 500 -fixy 2.3222 -dataset ./database/alanine-dipeptide-3x250ns-heavy-atom-positions.npz

Key Options

• -cuda: Which device to use with -1 standing for CPU, number bigger than -1 is N.O. of GPU;
• -hdim: Hidden dimension of mlps;
• -numFlow: Number of flows layers;
• -nlayers: Number of mlps layers in the rnvp;
• -nmlp: Number of dense layers in each mlp;
• -smile: SMILE expression of this molecular;
• -dataset: Path to the training data.

To see detailed options, run python density_estimation_md.py -h.

Analysis Notebook

Alanine Dipeptide

1.2 Image dataset

To train a neuralCT for machine learning dataset, use density_estimation.py.

python ./density_estimation.py -epochs 5000 -batch 200 -hdim 256 -nmlp 3 -nlayers 16 -dataset ./database/mnist.npz

Key Options

• -cuda: Which device to use with -1 standing for CPU, number bigger than -1 is N.O. of GPU;
• -hdim: Hidden dimension of mlps;
• -numFlow: Number of flows layers;
• -nlayers: Number of mlps layers in the rnvp;
• -nmlp: Number of dense layers in each mlp;
• -n: Number of dimensions of the training data;
• -dataset: Path to the training data.

To see detailed options, runpython density_estimation.py -h.

Analysis Notebook

MNIST concept compression

2. Variational Free Energy Calculation

To train a neuralCT via the variational approach, use variation.py. Specify the name of the distribution with the -source option.

python ./variation.py -epochs 5000 -batch 200 -hdim 256 -nmlp 3 -nlayers 16 -source Ring2d

Key Options

• -cuda: Which device to use with -1 standing for CPU, number bigger than -1 is N.O. of GPU;
• -hdim: Hidden dimension of mlps;
• -numFlow: Number of flows layers;
• -nlayers: Number of mlps layers in the rnvp;
• -nmlp: Number of dense layers in each mlp;
• -source: Using which source, Ring2d or HarmonicChain.

To see detailed options, run python variation.py -h.

Analysis Notebooks

1. Ring2D distribution
2. Harmonic Chain

Citation

@article{neuralCT,
  Author = {Shuo-Hui Li, Chen-Xiao Dong, Linfeng Zhang, and Lei Wang},
  Title = {Neural Canonical Transformation with Symplectic Flows},
  Year = {2019},
  Eprint = {arXiv:1910.00024},
}

Contact

For questions and suggestions, please contact Shuo-Hui Li at [email protected].