S. Hamdi, W. E. Schiesser, and G. W Griffiths. Method of lines. *Scholarpedia*, 2(7):2859, 2007. doi: 10.4249/scholarpedia.2859. revision #26511.
Xu Han, Han Gao, Tobias Pfaff, Jian-Xun Wang, and Liping Liu. Predicting physics in mesh-reduced space with temporal attention. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=XctLdNfCmP.
Pashupati Hegde, Cagatay Yildiz, Harri Lähdesmäki, Samuel Kaski, and Markus Heinonen. Variational multiple shooting for bayesian ODEs with gaussian processes. In The 38th Conference on Uncertainty in Artificial Intelligence, 2022. URL https://openreview.net/forum?id=r2NuhIUoceq.
Charles Hirsch. Numerical computation of internal and external flows: The fundamentals of computational fluid dynamics. Elsevier, 2007.
Philipp Holl, Vladlen Koltun, Kiwon Um, and Nils Thuerey. phiflow: A differentiable pde solving framework for deep learning via physical simulations. In NeurIPS Workshop on Differentiable vision, graphics, and physics applied to machine learning, 2020. URL https://montrealrobotics.ca/diffcvgp/ assets/papers/3.pdf.
Chuanbo Hua, Federico Berto, Michael Poli, Stefano Massaroli, and Jinkyoo Park. Efficient continuous spatio-temporal simulation with graph spline networks. In ICML 2022 2nd AI for Science Workshop, 2022. URL https://openreview.net/forum?id=PBTOVftuji.
Valerii Iakovlev, Cagatay Yildiz, Markus Heinonen, and Harri Lähdesmäki. Latent neural ODEs with sparse bayesian multiple shooting. In *The Eleventh International Conference on Learning Representations*, 2023. URL https://openreview.net/forum?id=moI1FZfj_1b.
Chiyu lMaxr Jiang, Soheil Esmaeilzadeh, Kamyar Azizzadenesheli, Karthik Kashinath, Mustafa Mustafa, Hamdi A. Tchelepi, Philip Marcus, Mr Prabhat, and Anima Anandkumar. Mesh-freeflownet: A physics-constrained deep continuous space-time super-resolution framework. SC20: International Conference for High Performance Computing, Networking, Storage and Analysis, Nov 2020. doi: 10.1109/sc41405.2020.00013. URL http://dx.doi.org/10.1109/SC41405.2020.00013.
Armand Jordana, Justin Carpentier, and Ludovic Righetti. Learning dynamical systems from noisy sensor measurements using multiple shooting, 2021.
E.J. Kansa. Multiquadrics—a scattered data approximation scheme with applications to computational fluid-dynamics—ii solutions to parabolic, hyperbolic and elliptic partial differential equations. Computers and Mathematics with Applications, 19(8):147-161, 1990. ISSN 0898-1221. doi: https://doi.org/10.1016/0898-1221(90)90271-K. URL https://www.sciencedirect.com/science/article/pii/089812219090271K.
Diederik P. Kingma and Jimmy Ba. Adam: A method for stochastic optimization, 2017.
Diederik P Kingma and Max Welling. Auto-encoding variational bayes, 2013.
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. doi: 10.1073/pnas.2101784118. URL https://www.pnas.org/doi/abs/10.1073/pnas.2101784118.
Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar. Fourier neural operator for parametric partial differential equations. In International Conference on Learning Representations, 2021. URL https://openreview.net/forum?id=c8P9NQVtmnO.
Marten Lienen and Stephan Gunnemann. Learning the dynamics of physical systems from sparse observations with finite element networks. In International Conference on Learning Representations, 2022. URL https://openreview.net/forum?id=HFmAukZ-k-2.