[15] Kathryn E. Brennan, Stephen L. Campbell, and Linda R. Petzold. Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. Society for Industrial and Applied Mathematics, 1995.
[16] Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. Proceedings of the National Academy of Sciences, 113(15):3932-3937, 2016.
[17] Mickaël D. Chekroun, Eric Simonnet, and Michael Ghil. Stochastic climate dynamics: Random attractors and time-dependent invariant measures. Physica D: Nonlinear Phenomena, 240(21): 1685-1700, 2011.
[18] Ricky T.Q. Chen, Yulia Rubanova, Jesse Bettencourt, and David K. Duvenaud. Neural ordinary differential equations. In Advances in Neural Information Processing Systems, pages 6571-6583, 2018.
[19] Yuhan Chen, Takashi Matsubara, and Takaharu Yaguchi. Neural symplectic form: learning Hamiltonian equations on general coordinate systems. pages 16659-16670, 2021.
[20] Zhijie Chen, Mingquan Feng, Junchi Yan, and Hongyuan Zha. Learning neural Hamiltonian dynamics: A methodological overview. arXiv preprint arXiv:2203.00128, 2022.
[21] Hong Sheng Chin. Stabilization Methods for Simulations of Constrained Multibody Dynamics. PhD thesis, University of British Columbia, 1995. URL https://open.library.ubc.ca/collections/ubctheses/831/items/1.0080031.
[22] Harald Cramer. Mathematical Methods of Statistics. Princeton University Press, 1999.
[23] Miles Cranmer. Interpretable machine learning for science with PySR and SymbolicRegression.jl. arXiv preprint arXiv:2305.01582, 2023.
[24] Miles Cranmer, Sam Greydanus, Stephan Hoyer, Peter Battaglia, David Spergel, and Shirley Ho. Lagrangian neural networks. arXiv preprint arXiv:2003.04630, 2020.
[25] George Cybenko. Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signals and Systems, 2(4):303-314, 1989.
[26] Raj Dandekar, Karen Chung, Vaibhav Dixit, Mohamed Tarek, Aslan Garcia-Valadez, Krishna Vishal Vemula, and Christopher Rackauckas. Bayesian neural ordinary differential equations. arXiv preprint arXiv:2012.07244, 2020.
[27] Simon Danisch and Julius Krumbiegel. Makie.jl: Flexible high-performance data visualization for Julia. Journal of Open Source Software, 6(65):3349, 2021.
[28] David Diego, Kristian Agasøster Haaga, and Bjarte Hannisdal. Transfer entropy computation using the Perron-Frobenius operator. Phys. Rev. E, 99:042212, 2019.
[29] Thai P. Duong and Nikolay A. Atanasov. Hamiltonian-based neural ODE networks on the SE(3) manifold for dynamics learning and control. In Proceedings of Robotics: Science and Systems, 2021.
[30] Emilien Dupont, Arnaud Doucet, and Yee Whye Teh. Augmented neural ODEs. In Advances in Neural Information Processing Systems, pages 3140-3150, 2019.
[31] Chris Finlay, Joern-Henrik Jacobsen, Levon Nurbekyan, and Adam Oberman. How to train your neural ODE: the world of Jacobian and kinetic regularization. In Proceedings of the 37th International Conference on Machine Learning, pages 3154-3164. PMLR, 2020.
[32] Marc Finzi, Ke Alexander Wang, and Andrew G Wilson. Simplifying Hamiltonian and Lagrangian neural networks via explicit constraints. In Advances in Neural Information Processing Systems, pages 13880-13889, 2020.
[33] Simone Fiori. Manifold calculus in system theory and control—fundamentals and first-order systems. Symmetry, 13(11), 2021.