[14] Lu Lu, Pangzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis. Learning nonlinear operators via deeponet based on the universal approximation theorem of operators. Nature Machine Intelligence, 3:218-229, 2021.
[15] Nikola Kovachki, Zongyi Li, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Neural operator: Learning maps between function spaces with applications to pdes. Journal of Machine Learning Research, 24(89):1-97, 2023.
[16] Walter Strauss. *Partial Differential Equations An Introduction*. John Wiley & Sons, 2007.
[17] Makoto Takamoto, Timothy Praditia, Raphael Leiteritz, Dan MacKinlay, Francesco Alesiani, Dirk Pflüger, and Mathias Niepert. PDEBench: An Extensive Benchmark for Scientific Machine Learning. In 36th Conference on Neural Information Processing Systems (NeurIPS 2022) Track on Datasets and Benchmarks, 2022.
[18] Karl Otness, Arvi Gjoka, Joan Bruna, Daniele Panozzo, Benjamin Peherstorfer, Teseo Schneider, and Denis Zorin. An extensible benchmark suite for learning to simulate physical systems. In 35th Conference on Neural Information Processing Systems (NeurIPS 2021) Track on Datasets and Benchmarks, 2021.
[19] Wai Tong Chung, Ki Sung Jung, Jacqueline H Chen, and Matthias Ihme. BLASTNet: A call for community-involved big data in combustion machine learning. Applications in Energy and Combustion Science, 12:100087, 2022.
[20] Florent Bonnet, Jocelyn Mazari, Paola Cinnella, and Patrick Gallinari. AirfRANS: High fidelity computational fluid dynamics dataset for approximating reynolds-averaged navier-stokes solutions. Advances in Neural Information Processing Systems, 35:23463-23478, 2022.
[21] Anshu Dubey, Klaus Weide, Jared O'Neal, Akash Dhruv, Sean Couch, J. Austin Harris, Tom Klosterman, Rajeev Jain, Johann Rudi, Bronson Messer, Michael Pajkos, Jared Carlson, Ran Chu, Mohamed Wahib, Saurabh Chawdhary, Paul M. Ricker, Dongwook Lee, Katie Antypas, Katherine M. Riley, Christopher Daley, Murali Ganapathy, Francis X. Timmes, Dean M. Townsley, Marcos Vanella, John Bachan, Paul M. Rich, Shravan Kumar, Eirik Endeve, W. Raphael Hix, Anthony Mezzacappa, and Thomas Papatheodore. Flash-X: A multiphysics simulation software instrument. SoftwareX, 19:101168, 2022.
[22] Kimberly L. Stachenfeld, Drummond B. Fielding, Dmitrii Kochkov, M. Cranmer, Tobias Pfaff, Jonathan Godwin, Can Cui, Shi-Lin Ho, Peter W. Battaglia, and Alvaro Sanchez-Gonzalez. Learned coarse models for efficient turbulence simulation. ICLR, 2022.
[23] Hans Hersbach, Bill Bell, Paul Berrisford, Shoji Hirahara, András Horányi, Joaquín Muñoz-Sabater, Julien Nicolas, Carole Peubey, Raluca Radu, Dinand Schepers, et al. The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146(730):1999-2049, 2020.
[24] Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, et al. FourCastNet: A global data-driven high-resolution weather model using adaptive fourier neural operators. arXiv preprint arXiv:2202.11214, 2022.
[25] Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Winsberger, Meire Fortunato, Alexander Pritzel, Suman Ravuri, Timo Ewalds, Ferran Alet, Zach Eaton-Rosen, et al. GraphCast: Learning skillful medium-range global weather forecasting. arXiv preprint arXiv:2212.12794, 2022.
[26] Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K Gupta, and Aditya Grover. ClimaX: A foundation model for weather and climate. arXiv preprint arXiv:2301.10343, 2023.
[27] Dmitrii Kochkov, Jamie A Smith, Ayya Alieva, Qing Wang, Michael P Brenner, and Stephan Hoyer. Machine learning-accelerated computational fluid dynamics. Proceedings of the National Academy of Sciences, 118(21):e2101784118, 2021.
[28] Phillip Lippe, Bastiaan S. Veeling, Paris Perdikaris, Richard E Turner, and Johannes Brandstetter. Modeling accurate long rollouts with temporal neural PDE solvers. In ICML Workshop on New Frontiers in Learning, Control, and Dynamical Systems, 2023.