Numerical Calabi-Yau metrics from holomorphic networks

Michael Douglas, Subramanian Lakshminarasimhan, Yidi Qi
Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, PMLR 145:223-252, 2022.

Abstract

We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat Ka ̈hler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with little or no symmetry. We also discuss issues such as overparameterization and choice of optimization methods.

Cite this Paper

BibTeX
@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}, abstract = {We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat Ka ̈hler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with little or no symmetry. We also discuss issues such as overparameterization and choice of optimization methods. } }
Endnote
%0 Conference Paper %T Numerical Calabi-Yau metrics from holomorphic networks %A Michael Douglas %A Subramanian Lakshminarasimhan %A Yidi Qi %B Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference %C Proceedings of Machine Learning Research %D 2022 %E Joan Bruna %E Jan Hesthaven %E Lenka Zdeborova %F pmlr-v145-douglas22a %I PMLR %P 223--252 %U https://proceedings.mlr.press/v145/douglas22a.html %V 145 %X We propose machine learning inspired methods for computing numerical Calabi-Yau (Ricci flat Ka ̈hler) metrics, and implement them using Tensorflow/Keras. We compare them with previous work, and find that they are far more accurate for manifolds with little or no symmetry. We also discuss issues such as overparameterization and choice of optimization methods.
APA
Douglas, M., Lakshminarasimhan, S. & Qi, Y.. (2022). Numerical Calabi-Yau metrics from holomorphic networks. Proceedings of the 2nd Mathematical and Scientific Machine Learning Conference, in Proceedings of Machine Learning Research 145:223-252 Available from https://proceedings.mlr.press/v145/douglas22a.html.

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