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Physics-informed machine learning (PIML) has emerged as a promising alternative to classical methods for predicting dynamical systems, offering faster and more generalizable solutions.
Deterministic nonperiodic flow
Edward N Lorenz · 1963
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Determining Lyapunov exponents from a time series
Alan Wolf, Jack B Swift, Harry L Swinney, and John A Vastano · 1985
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Approximation of dynamical systems by continuous time recurrent neural networks
Ken-ichi Funahashi and Yuichi Nakamura · 1993
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Learning long-term dependencies with gradient descent is difficult
Yoshua Bengio, Patrice Simard, and Paolo Frasconi · 1994
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Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
Tianping Chen and Hong Chen · 1995
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Long short-term memory
Sepp Hochreiter and Jürgen Schmidhuber · 1997
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Predictive pharmacokinetic-pharmacodynamic modeling of tumor growth kinetics in xenograft models after administration of anticancer agents
Monica Simeoni, Paolo Magni, Cristiano Cammia, Giuseppe De Nicolao, Valter Croci, Enrico Pesenti, Massimiliano Germani, Italo Poggesi, and Maurizio Rocchetti · 2004
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On the difficulty of training recurrent neural networks
Razvan Pascanu, Tomas Mikolov, and Yoshua Bengio · 2013
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Learning phrase representations using RNN encoder–decoder for statistical machine translation
Kyunghyun Cho, Bart van Merriënboer, Çağlar Gulçehre, Dzmitry Bahdanau, Fethi Bougares, Holger Schwenk, and Yoshua Bengio · 2014
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Sequence to sequence learning with neural networks
Ilya Sutskever, Oriol Vinyals, and Quoc V Le · 2014
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Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2015
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Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton · 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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Attention is all you need
Ashish Vaswani, Noam Shazeer, Niki Parmar, Jakob Uszkoreit, Llion Jones, Aidan N Gomez, Łukasz Kaiser, and Illia Polosukhin · 2017
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Bert: Pre-training of deep bidirectional transformers for language understanding
Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova · 2018
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Can recurrent neural networks warp time?
Corentin Tallec and Yann Ollivier · 2018
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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Language models are few-shot learners
Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al · 2020
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Transformers are RNNs: Fast autoregressive transformers with linear attention
Angelos Katharopoulos, Apoorv Vyas, Nikolaos Pappas, and François Fleuret · 2020
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Backpropagation algorithms and reservoir computing in recurrent neural networks for the forecasting of complex spatiotemporal dynamics
Pantelis-Rafail Vlachas, Jaideep Pathak, Brian R Hunt, Themistoklis P Sapsis, Michelle Girvan, Edward Ott, and Petros Koumoutsakos · 2020
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Choose a Transformer: Fourier or Galerkin
Shuhao Cao · 2021
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Efficiently modeling long sequences with structured state spaces
Albert Gu, Karan Goel, and Christopher Ré · 2021
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Physics-informed machine learning
George Em Karniadakis, Ioannis G Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang · 2021
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Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Borislavov Kovachki, Kamyar Azizzadenesheli, Burigede liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2021
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GNOT: A general neural operator transformer for operator learning
Zhongkai Hao, Zhengyi Wang, Hang Su, Chengyang Ying, Yinpeng Dong, Songming Liu, Ze Cheng, Jian Song, and Jun Zhu · 2023
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Augmented physics-informed neural networks (APINNs): A gating network-based soft domain decomposition methodology
Zheyuan Hu, Ameya D Jagtap, George Em Karniadakis, and Kenji Kawaguchi · 2023
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Transformer for partial differential equations’ operator learning
Zijie Li, Kazem Meidani, and Amir Barati Farimani · 2023
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Katarzyna Michałowska, Somdatta Goswami, George Em Karniadakis, and Signe Riemer-Sørensen · 2023
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Ditto: Diffusion-inspired temporal transformer operator
Oded Ovadia, Eli Turkel, Adar Kahana, and George Em Karniadakis · 2023
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Zongyi Li, Miguel Liu-Schiaffini, Nikola Kovachki, Burigede Liu, Kamyar Azizzadenesheli, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2021
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Swin transformer: Hierarchical vision transformer using shifted windows
Ze Liu, Yutong Lin, Yue Cao, Han Hu, Yixuan Wei, Zheng Zhang, Stephen Lin, and Baining Guo · 2021
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Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators
Lu Lu, Pengzhan Jin, Guofei Pang, Zhongqiang Zhang, and George Em Karniadakis · 2021
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Physics-incorporated convolutional recurrent neural networks for source identification and forecasting of dynamical systems
Priyabrata Saha, Saurabh Dash, and Saibal Mukhopadhyay · 2021
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Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
Sifan Wang, Hanwen Wang, and Paris Perdikaris · 2021
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Approximation rates of DeepONets for learning operators arising from advection–diffusion equations
Beichuan Deng, Yeonjong Shin, Lu Lu, Zhongqiang Zhang, and George Em Karniadakis · 2022
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Hungry hungry hippos: Towards language modeling with state space models
Daniel Y Fu, Tri Dao, Khaled K Saab, Armin W Thomas, Atri Rudra, and Christopher Ré · 2022
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HNO: Hyena neural operator for solving PDEs
Saurabh Patil, Zijie Li, and Amir Barati Farimani · 2023
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RWKV: Reinventing RNNs for the transformer era
Bo Peng, Eric Alcaide, Quentin Anthony, Alon Albalak, Samuel Arcadinho, Stella Biderman, Huanqi Cao, Xin Cheng, Michael Chung, Matteo Grella, et al · 2023
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Hyena hierarchy: Towards larger convolutional language models
Michael Poli, Stefano Massaroli, Eric Nguyen, Daniel Y Fu, Tri Dao, Stephen Baccus, Yoshua Bengio, Stefano Ermon, and Christopher Re · 2023
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Khemraj Shukla, Vivek Oommen, Ahmad Peyvan, Michael Penwarden, Luis Bravo, Anindya Ghoshal, Robert M Kirby, and George Em Karniadakis · 2023
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Retentive network: A successor to transformer for large language models
Yutao Sun, Li Dong, Shaohan Huang, Shuming Ma, Yuqing Xia, Jilong Xue, Jianyong Wang, and Furu Wei · 2023
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Reliable extrapolation of deep neural operators informed by physics or sparse observations
Min Zhu, Handi Zhang, Anran Jiao, George Em Karniadakis, and Lu Lu · 2023
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Laplace neural operator for solving differential equations
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