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Neural ordinary differential equations (Neural ODEs) are a new family of deep-learning models with continuous depth.
Mathematical theory of optimal processes
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Hamiltonian systems: chaos and quantization
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Construction of higher order symplectic integrators
Haruo Yoshida · 1990
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Solving ordinary differential equations II
Gerhard Wanner and Ernst Hairer · 1996
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Determinants of block matrices
John R Silvester · 2000
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An introduction to numerical analysis
Endre Süli and David F Mayers · 2003
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Neural controlled differential equations for irregular time series
Patrick Kidger, James Morrill, James Foster, and Terry Lyons · 2005
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“Hey, that’s not an ODE”: Faster ODE Adjoints with 12 Lines of Code
Patrick Kidger, Ricky T. Q. Chen, and Terry Lyons · 2009
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An asynchronous leapfrog method ii
Ulrich Mutze · 2013
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On the difficulty of training recurrent neural networks
Razvan Pascanu, Tomas Mikolov, and Yoshua Bengio · 2013
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Explaining and harnessing adversarial examples
Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy · 2014
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Density estimation using real nvp
Laurent Dinh, Jascha Sohl-Dickstein, and Samy Bengio · 2016
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Deep residual learning for image recognition
Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun · 2016
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Stable architectures for deep neural networks
Eldad Haber and Lars Ruthotto · 2017
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Train cifar10 with pytorch
Kuang Liu · 2017
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A proposal on machine learning via dynamical systems
E Weinan · 2017
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Neural ordinary differential equations
Ricky TQ Chen, Yulia Rubanova, Jesse Bettencourt, and David K Duvenaud · 2018
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Ffjord: Free-form continuous dynamics for scalable reversible generative models
Will Grathwohl, Ricky TQ Chen, Jesse Bettencourt, Ilya Sutskever, and David Duvenaud · 2018
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Glow: Generative flow with invertible 1x1 convolutions
Durk P Kingma and Prafulla Dhariwal · 2018
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Snode: Spectral discretization of neural odes for system identification
Alessio Quaglino, Marco Gallieri, Jonathan Masci, and Jan Koutník · 2019
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Latent ordinary differential equations for irregularly-sampled time series
Yulia Rubanova, Ricky TQ Chen, and David K Duvenaud · 2019
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Deep neural networks motivated by partial differential equations
Lars Ruthotto and Eldad Haber · 2019
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Hamiltonian graph networks with ode integrators
Alvaro Sanchez-Gonzalez, Victor Bapst, Kyle Cranmer, and Peter Battaglia · 2019
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Unconstrained monotonic neural networks
Antoine Wehenkel and Gilles Louppe · 2019
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Beyond finite layer neural networks: Bridging deep architectures and numerical differential equations
Yiping Lu, Aoxiao Zhong, Quanzheng Li, and Bin Dong · 2018
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Yuval Tassa, Yotam Doron, Alistair Muldal, Tom Erez, Yazhe Li, Diego de Las Casas, David Budden, Abbas Abdolmaleki, Josh Merel, Andrew Lefrancq, et al · 2018
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Invertible residual networks
Jens Behrmann, Will Grathwohl, Ricky TQ Chen, David Duvenaud, and Jörn-Henrik Jacobsen · 2019
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Residual flows for invertible generative modeling
Ricky TQ Chen, Jens Behrmann, David K Duvenaud, and Jörn-Henrik Jacobsen · 2019
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Augmented neural odes
Emilien Dupont, Arnaud Doucet, and Yee Whye Teh · 2019
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On robustness of neural ordinary differential equations
YAN Hanshu, DU Jiawei, TAN Vincent, and FENG Jiashi · 2019
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Yaofeng Desmond Zhong, Biswadip Dey, and Amit Chakraborty · 2019
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Interpolated adjoint method for neural odes
Talgat Daulbaev, Alexandr Katrutsa, Larisa Markeeva, Julia Gusak, Andrzej Cichocki, and Ivan Oseledets · 2020
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How to train your neural ode: the world of jacobian and kinetic regularization
Chris Finlay, Jörn-Henrik Jacobsen, Levon Nurbekyan, and Adam M Oberman · 2020
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Scalable gradients for stochastic differential equations
Xuechen Li, Ting-Kam Leonard Wong, Ricky TQ Chen, and David Duvenaud · 2020
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Stefano Massaroli, Michael Poli, Jinkyoo Park, Atsushi Yamashita, and Hajime Asama · 2020
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Continuous-in-depth neural networks
Alejandro F Queiruga, N Benjamin Erichson, Dane Taylor, and Michael W Mahoney · 2020
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A machine learning framework for solving high-dimensional mean field game and mean field control problems
Lars Ruthotto, Stanley J Osher, Wuchen Li, Levon Nurbekyan, and Samy Wu Fung · 2020
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Universal approximation power of deep neural networks via nonlinear control theory
Paulo Tabuada and Bahman Gharesifard · 2020
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Adaptive checkpoint adjoint method for gradient estimation in neural ode
Juntang Zhuang, Nicha Dvornek, Xiaoxiao Li, Sekhar Tatikonda, Xenophon Papademetris, and James Duncan · 2020
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