[54] Mario Lezcano-Casado and David Martínez-Rubio. Cheap orthogonal constraints in neural networks: A simple parametrization of the orthogonal and unitary group. In Proceedings of the 36th International Conference on Machine Learning, pages 3794-3803. PMLR, 2019.
[55] Yi Heng Lim and Muhammad Firmansyah Kasim. Unifying physical systems' inductive biases in neural ODE using dynamics constraints. arXiv preprint arXiv:2208.02632, 2022.
[56] Ilya Loshchilov and Frank Hutter. Decoupled weight decay regularization. In 7th International Conference on Learning Representations, 2019.
[57] Aaron Lou, Derek Lim, Isay Katsman, Leo Huang, Qingxuan Jiang, Ser Nam Lim, and Christopher M. De Sa. Neural manifold ordinary differential equations. In Advances in Neural Information Processing Systems, pages 17548-17558, 2020.
[58] Michael Lutter, Christian Ritter, and Jan Peters. Deep Lagrangian networks: Using physics as model prior for deep learning. In 7th International Conference on Learning Representations, 2019.
[59] Yingbo Ma, Vaibhav Dixit, Michael J Innes, Xingjian Guo, and Christopher Rackauckas. A comparison of automatic differentiation and continuous sensitivity analysis for derivatives of differential equation solutions. In 2021 IEEE High Performance Extreme Computing Conference (HPEC), pages 1-9. IEEE, 2021.
[60] Emile Mathieu and Maximilian Nickel. Riemannian continuous normalizing flows. In Advances in Neural Information Processing Systems, pages 2503-2515, 2020.
[61] Y. Nishimori. Learning algorithm for independent component analysis by geodesic flows on orthogonal group. In IJCNN'99. International Joint Conference on Neural Networks. Proceedings (Cat. No.99CH36339), volume 2, pages 933-938 vol.2, 1999. doi: 10.1109/IJCNN.1999.831078.
[62] Alexander Norcliffe, Cristian Bodnar, Ben Day, Nikola Simidjievski, and Pietro Liò. On second order behaviour in augmented neural ODEs. In Advances in Neural Information Processing Systems, pages 5911-5921, 2020.
[63] Avik Pal, Yingbo Ma, Viral Shah, and Christopher Rackauckas. Opening the blackbox: Accelerating neural differential equations by regularizing internal solver heuristics. In Proceedings of the 38th International Conference on Machine Learning, pages 8325-8335. PMLR, 2021.
[64] Suhan Park, Mathew Schwartz, and Jaeheung Park. NODE IK: Solving inverse kinematics with neural ordinary differential equations for path planning. arXiv preprint arXiv:2209.00498, 2022.
[65] Linda Petzold. Differential/algebraic equations are not ODE's. SIAM Journal on Scientific and Statistical Computing, 3(3):367-384, 1982.
[66] Christopher Rackauckas and Qing Nie. Differential Equations.jl-a performant and feature-rich ecosystem for solving differential equations in Julia. Journal of Open Research Software, 5(1), 2017.
[67] Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, and Alan Edelman. Universal differential equations for scientific machine learning. arXiv preprint arXiv:2001.04385, 2020.
[68] Danilo Jimenez Rezende, George Papamakarios, Sebastien Racaniere, Michael Albergo, Gurtej Kanwar, Phiala Shanahan, and Kyle Cranmer. Normalizing flows on tori and spheres. In Proceedings of the 37th International Conference on Machine Learning, pages 8083-8092. PMLR, 2020.
[69] Noam Rozen, Aditya Grover, Maximilian Nickel, and Yaron Lipman. Moser flow: Divergence-based generative modeling on manifolds. In Advances in Neural Information Processing Systems, pages 17669-17680, 2021.