Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere

Boris Bonev, Thorsten Kurth, Christian Hundt, Jaideep Pathak, Maximilian Baust, Karthik Kashinath, Anima Anandkumar
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:2806-2823, 2023.

Abstract

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates by incorrectly assuming flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmo- spheric dynamics, and demonstrate stable autoregressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

Cite this Paper


BibTeX
@InProceedings{pmlr-v202-bonev23a, title = {Spherical {F}ourier Neural Operators: Learning Stable Dynamics on the Sphere}, author = {Bonev, Boris and Kurth, Thorsten and Hundt, Christian and Pathak, Jaideep and Baust, Maximilian and Kashinath, Karthik and Anandkumar, Anima}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {2806--2823}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/bonev23a/bonev23a.pdf}, url = {https://proceedings.mlr.press/v202/bonev23a.html}, abstract = {Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates by incorrectly assuming flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmo- spheric dynamics, and demonstrate stable autoregressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.} }
Endnote
%0 Conference Paper %T Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere %A Boris Bonev %A Thorsten Kurth %A Christian Hundt %A Jaideep Pathak %A Maximilian Baust %A Karthik Kashinath %A Anima Anandkumar %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-bonev23a %I PMLR %P 2806--2823 %U https://proceedings.mlr.press/v202/bonev23a.html %V 202 %X Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates by incorrectly assuming flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmo- spheric dynamics, and demonstrate stable autoregressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.
APA
Bonev, B., Kurth, T., Hundt, C., Pathak, J., Baust, M., Kashinath, K. & Anandkumar, A.. (2023). Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:2806-2823 Available from https://proceedings.mlr.press/v202/bonev23a.html.

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