[1] Juan Lopez Alcaraz and Nils Strodthoff. Diffusion-based time series imputation and forecasting with structured state space models. Transactions on Machine Learning Research, 2023. ISSN 2835-8856. URL https://openreview.net/forum?id=hHiIbk7ApW.
[2] Arpit Bansal, Eitan Borgnia, Hong-Min Chu, Jie S. Li, Hamid Kazemi, Furong Huang, Micah Goldblum, Jonas Geiping, and Tom Goldstein. Cold diffusion: Inverting arbitrary image transforms without noise. Advances in Neural Information Processing Systems, 2023.
[3] Peter Bauer, Alan Thorpe, and Gilbert Brunet. The quiet revolution of numerical weather prediction. Nature, 525(7567):47-55, Sep 2015. ISSN 1476-4687. doi: 10.1038/nature14956. URL https://doi.org/10.1038/nature14956.
[4] Emanuele Bevacqua, Laura Suarez-Gutierrez, Aglaé Jézquel, Flavio Lehner, Mathieu Vrac, Pascal Yiou, and Jakob Zscheischler. Advancing research on compound weather and climate events via large ensemble model simulations. Nature Communications, 14(1):2145, April 2023.
[5] Johannes Brandstetter, Daniel E. Worrall, and Max Welling. Message passing neural PDE solvers. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=vSix3HPYKSU.
[6] Johannes Brandstetter, Rianne van den Berg, Max Welling, and Jayesh K Gupta. Clifford neural layers for PDE modeling. In The Eleventh International Conference on Learning Representations, 2023. URL https://openreview.net/forum?id=okwxL_c4x84.
[7] Casey M Brown, Jay R Lund, Ximing Cai, Patrick M Reed, Edith A Zagona, Avi Ostfeld, Jim Hall, Gregory W Characklis, Winston Yu, and Levi Brekke. The future of water resources systems analysis: Toward a scientific framework for sustainable water management. Water resources research, 51(8):6110-6124, 2015.
[8] Ashesh Chattopadhyay and Pedram Hassanzadeh. Why are deep learning-based models of geophysical turbulence long-term unstable? NeurIPS, Machine Learning for Physical Sciences, 2022.
[9] Ashesh Chattopadhyay, Mustafa Mustafa, Pedram Hassanzadeh, and Karthik Kashinath. Deep spatial transformers for autoregressive data-driven forecasting of geophysical turbulence. In Proceedings of the 10th International Conference on Climate Informatics, pages 106-112, 2020.
[10] Giannis Daras, Maurizio Delbracio, Hossein Talebi, Alexandros G. Dimakis, and Peyman Milanfar. Soft diffusion: Score matching for general corruptions. 2022. URL https://arxiv.org/abs/2209.05442.
[11] Emmanuel de Bézenac, Arthur Pajot, and Patrick Gallinari. Deep learning for physical processes: Incorporating prior scientific knowledge. In International Conference on Learning Representations, 2018. URL https://openreview.net/forum?id=By4HsfWAZ.
[12] Emmanuel de Bézenac, Syama Sundar Rangapuram, Konstantinos Benidis, Michael Bohlke-Schneider, Richard Kurle, Lorenzo Stella, Hilaf Hasson, Patrick Gallinari, and Tim Januschowski. Normalizing kalman filters for multivariate time series analysis. In Advances in Neural Information Processing Systems, volume 33, pages 2995-3007, 2020. URL https://proceedings.neurips.cc/paper_files/paper/2020/file/1f47cef5e38c952f94c5d61726027439-Paper.pdf.
[13] Laurent El Ghaoui, Fangda Gu, Bertrand Travacca, Armin Askari, and Alicia Tsai. Implicit deep learning. SIAM Journal on Mathematics of Data Science, 3(3):930-958, 2021.
[14] N. Benjamin Erichson, Michael Muehlebach, and Michael W. Mahoney. Physics-informed autoencoders for lyapunov-stable fluid flow prediction. 2019. URL https://arxiv.org/abs/1905.10866.
[15] Lasse Espeholt, Shreya Agrawal, Casper Sønderby, Manoj Kumar, Jonathan Heek, Carla Bromberg, Cenk Gazen, Rob Carver, Marcin Andrychowicz, Jason Hickey, Aaron Bell, and Nal Kalchbrenner. Deep learning for twelve hour precipitation forecasts. Nature Communications, 13(1):5145, Sep 2022. ISSN 2041-1723. doi: 10.1038/s41467-022-32483-x. URL https://doi.org/10.1038/s41467-022-32483-x.
[16] V. Fortin, M. Abaza, F. Anctil, and R. Turcotte. Why should ensemble spread match the rmse of the ensemble mean? Journal of Hydrometeorology, 15(4):1708 - 1713, 2014. doi: