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The infinite-depth paradigm pioneered by Neural ODEs has launched a renaissance in the search for novel dynamical system-inspired deep learning primitives; however, their utilization in problems of non-trivial size has often proved impossible due to poor computational scalability.
A user’s view of solving stiff ordinary differential equations
L. F. Shampine and C. W. Gear · 1979
Earlier work this paper cites.
A family of embedded runge-kutta formulae
J. R. Dormand and P. J. Prince · 1980
Earlier work this paper cites.
High order embedded runge-kutta formulae
P. J. Prince and J. R. Dormand · 1981
Earlier work this paper cites.
Artificial neural network methods in quantum mechanics
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 1997
Earlier work this paper cites.
Neuroanimator: Fast neural network emulation and control of physics-based models
R. Grzeszczuk, D. Terzopoulos, and G. Hinton · 1998
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 1998
Earlier work this paper cites.
S. Massaroli, M. Poli, J. Park, A. Yamashita, and H. Asama · 2002
Earlier work this paper cites.
Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations
J. Cash · 2003
Earlier work this paper cites.
Precomputing interactive dynamic deformable scenes
D. L. James and K. Fatahalian · 2003
Earlier work this paper cites.
S. Massaroli, M. Poli, M. Bin, J. Park, A. Yamashita, and H. Asama · 2003
Earlier work this paper cites.
An introduction to numerical analysis
E. Süli and D. F. Mayers · 2003
Earlier work this paper cites.
The algorithm of neural networks on the initial value problems in ordinary differential equations
X. Li-ying, W. Hui, and Z. Zhe-zhao · 2007
Earlier work this paper cites.
Modeling ship equations of roll motion using neural networks
Z. Xing and L. McCue · 2010
Earlier work this paper cites.
TEXPLORE: Temporal Difference Reinforcement Learning for Robots and Time-Constrained Domains
T. Hester · 2013
Earlier work this paper cites.
Nonlinearly activated neural network for solving time-varying complex sylvester equation
S. Li and Y. Li · 2013
Earlier work this paper cites.
Comparison of artificial neural network architecture in solving ordinary differential equations
S. Mall and S. Chakraverty · 2013
Earlier work this paper cites.
A comprehensive review of stability analysis of continuous-time recurrent neural networks
H. Zhang, Z. Wang, and D. Liu · 2014
Earlier work this paper cites.
Delving deep into rectifiers: Surpassing human-level performance on imagenet classification
K. He, X. Zhang, S. Ren, and J. Sun · 2015
Earlier work this paper cites.
Numerical methods for ordinary differential equations
J. C. Butcher · 2016
Earlier work this paper cites.
Domain-adversarial training of neural networks
Y. Ganin, E. Ustinova, H. Ajakan, P. Germain, H. Larochelle, F. Laviolette, M. Marchand, and V. Lempitsky · 2016
Earlier work this paper cites.
Multi-level residual networks from dynamical systems view
B. Chang, L. Meng, E. Haber, F. Tung, and D. Begert · 2017
Earlier work this paper cites.
Principles of riemannian geometry in neural networks
M. Hauser and A. Ray · 2017
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Decoupled weight decay regularization
I. Loshchilov and F. Hutter · 2017
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Y. Lu, A. Zhong, Q. Li, and B. Dong · 2017
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Automatic differentiation in pytorch
A. Paszke, S. Gross, S. Chintala, G. Chanan, E. Yang, Z. DeVito, Z. Lin, A. Desmaison, L. Antiga, and A. Lerer · 2017
Cited alongside, same era.
Double continuum limit of deep neural networks
S. Sonoda and N. Murata · 2017
Cited alongside, same era.
Neural ordinary differential equations
Hamiltonian neural networks
S. Greydanus, M. Dzamba, and J. Yosinski · 2019
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Neural jump stochastic differential equations
J. Jia and A. R. Benson · 2019
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Switchnet: a neural network model for forward and inverse scattering problems
Y. Khoo and L. Ying · 2019
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Normalizing flows: Introduction and ideas
I. Kobyzev, S. Prince, and M. A. Brubaker · 2019
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Pde-net 2.0: Learning pdes from data with a numeric-symbolic hybrid deep network
Z. Long, Y. Lu, and B. Dong · 2019
Later among the works it cites.
Continual lifelong learning with neural networks: A review
G. I. Parisi, R. Kemker, J. L. Part, C. Kanan, and S. Wermter · 2019
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Graph neural ordinary differential equations
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Data driven governing equations approximation using deep neural networks
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Ç. Yıldız, M. Heinonen, and H. Lähdesmäki · 2019
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