暂无分享,去创建一个
Kamyar Azizzadenesheli | Anima Anandkumar | Kaushik Bhattacharya | Nikola Kovachki | Nikola B. Kovachki | Andrew Stuart | Burigede Liu | Zongyi Li | K. Azizzadenesheli | Anima Anandkumar | Zong-Yi Li | Burigede Liu | K. Bhattacharya | Andrew Stuart | Andrew M. Stuart
[1] Razvan Pascanu,et al. Sobolev Training for Neural Networks , 2017, NIPS.
[2] Maziar Raissi,et al. Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations , 2018, J. Mach. Learn. Res..
[3] Nicholas Geneva,et al. Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks , 2019, J. Comput. Phys..
[4] Chun Zhang,et al. Long-term prediction of chaotic systems with machine learning , 2020 .
[5] Jürgen Schmidhuber,et al. Learning to Forget: Continual Prediction with LSTM , 2000, Neural Computation.
[6] Ryan P. Adams,et al. Learning Composable Energy Surrogates for PDE Order Reduction , 2020, NeurIPS.
[7] Andrew M. Stuart,et al. Runge-Kutta methods for dissipative and gradient dynamical systems , 1994 .
[8] Kamyar Azizzadenesheli,et al. Neural Operator: Learning Maps Between Function Spaces , 2021, arXiv.org.
[9] Stephan Hoyer,et al. Learning data-driven discretizations for partial differential equations , 2018, Proceedings of the National Academy of Sciences.
[10] Stephanie Boehm,et al. Chaos Making A New Science , 2016 .
[11] Jaideep Pathak,et al. Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics , 2019, Neural Networks.
[12] Catherine E. Powell,et al. An Introduction to Computational Stochastic PDEs , 2014 .
[13] Jaideep Pathak,et al. Model-Free Prediction of Large Spatiotemporally Chaotic Systems from Data: A Reservoir Computing Approach. , 2018, Physical review letters.
[14] Kamyar Azizzadenesheli,et al. Fourier Neural Operator for Parametric Partial Differential Equations , 2021, ICLR.
[15] Lloyd N. Trefethen,et al. Fourth-Order Time-Stepping for Stiff PDEs , 2005, SIAM J. Sci. Comput..
[16] Thomas Brox,et al. U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.
[18] Grigorios A. Pavliotis,et al. Multiscale Methods: Averaging and Homogenization , 2008 .
[19] David Duvenaud,et al. Neural Ordinary Differential Equations , 2018, NeurIPS.
[20] Dit-Yan Yeung,et al. Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting , 2015, NIPS.
[21] Kamyar Azizzadenesheli,et al. Neural Operator: Graph Kernel Network for Partial Differential Equations , 2020, ICLR 2020.
[22] Javier Jiménez,et al. The turbulent cascade in five dimensions , 2017, Science.
[23] Steven L. Brunton,et al. Data-Driven Stabilization of Periodic Orbits , 2020, IEEE Access.
[24] Gary J. Chandler,et al. Invariant recurrent solutions embedded in a turbulent two-dimensional Kolmogorov flow , 2013, Journal of Fluid Mechanics.
[25] G. Sviridyuk. On the general theory of operator semigroups , 1994 .
[26] Mark Holland,et al. Central limit theorems and invariance principles for Lorenz attractors , 2007 .
[27] Yoshua Bengio,et al. Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling , 2014, ArXiv.
[28] Petros Koumoutsakos,et al. Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks , 2018, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
[29] A. Stuart. Perturbation Theory for Infinite Dimensional Dynamical Systems , 1995 .
[30] Alexander Smits,et al. High–Reynolds Number Wall Turbulence , 2011 .
[31] R. Temam. Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .
[32] Kunihiko Taira,et al. Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows , 2020, Journal of Fluid Mechanics.