MLGeometry

Higher dimensional computational geometry using machine learning software

• Kahler geometry and Kahler-Einstein metrics

More to come.

Set up the environment

1. Install conda via Anaconda or Miniconda

2. Install the jupyter notebook in the base environment:

   conda install -c conda-forge notebook
   conda install -c conda-forge nb_conda_kernels
   conda install -c conda-forge cudatoolkit=11.8.0
   

3. Create the environment with necessary packages:

   conda create -n MLGeometry pip tensorflow-probability==0.14.0 sympy matplotlib ipykernel
   

4. Activate the environment and install Tensorflow:

   conda activate MLGeometry
   python3 -m pip install nvidia-cudnn-cu11==8.6.0.163 tensorflow==2.12.*
   mkdir -p $CONDA_PREFIX/etc/conda/activate.d
   echo 'CUDNN_PATH=$(dirname $(python -c "import nvidia.cudnn;print(nvidia.cudnn.__file__)"))' >> $CONDA_PREFIX/etc/conda/activate.d/env_vars.sh
   echo 'export LD_LIBRARY_PATH=$CONDA_PREFIX/lib/:$CUDNN_PATH/lib:$LD_LIBRARY_PATH' >> $CONDA_PREFIX/etc/conda/activate.d/env_vars.sh
   source $CONDA_PREFIX/etc/conda/activate.d/env_vars.sh
   

5. Verify install:

   python3 -c "import tensorflow as tf; print(tf.config.list_physical_devices('GPU'))"
   

6. Open Jupyter with jupyter-notebook in the command line, and change the kernel in Kernel -> Change kernel -> Python [conda env:MLGeometry]

7. Clone the repository

   git clone https://github.com/yidiq7/MLGeometry/
   

   Or download the released version here

Sample jupyter notebook

Citation

You can find our paper on arxiv or PMLR. If you find our paper or package useful in your research or project, please cite it as follows:

@InProceedings{pmlr-v145-douglas22a,
  title = 	 {Numerical Calabi-Yau metrics from holomorphic networks},
  author =       {Douglas, Michael and Lakshminarasimhan, Subramanian and Qi, Yidi},
  booktitle = 	 {Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference},
  pages = 	 {223--252},
  year = 	 {2022},
  editor = 	 {Bruna, Joan and Hesthaven, Jan and Zdeborova, Lenka},
  volume = 	 {145},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {16--19 Aug},
  publisher =    {PMLR},
  pdf = 	 {https://proceedings.mlr.press/v145/douglas22a/douglas22a.pdf},
  url = 	 {https://proceedings.mlr.press/v145/douglas22a.html},
}