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Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs).
Approximation by superpositions of a sigmoidal function
George Cybenko · 1989
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Approximation capabilities of multilayer feedforward networks
Kurt Hornik · 1991
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A practical guide to pseudospectral methods
Bengt Fornberg · 1998
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Artificial neural networks for solving ordinary and partial differential equations
Isaac E Lagaris, Aristidis Likas, and Dimitrios I Fotiadis · 1998
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Finite element method
Klaus-Jürgen Bathe · 2007
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Deep sparse rectifier neural networks
Xavier Glorot, Antoine Bordes, and Yoshua Bengio · 2011
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Convolutional sequence to sequence learning
Jonas Gehring, Michael Auli, David Grangier, Denis Yarats, and Yann N Dauphin · 2017
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Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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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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Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and Weinan E · 2018
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Improving language understanding by generative pre-training
Alec Radford, Karthik Narasimhan, Tim Salimans, Ilya Sutskever, et al · 2018
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Deep hidden physics models: Deep learning of nonlinear partial differential equations
Maziar Raissi · 2018
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Machine learning and the physical sciences
Giuseppe Carleo, Ignacio Cirac, Kyle Cranmer, Laurent Daudet, Maria Schuld, Naftali Tishby, Leslie Vogt-Maranto, and Lenka Zdeborová · 2019
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Generating long sequences with sparse transformers
Rewon Child, Scott Gray, Alec Radford, and Ilya Sutskever · 2019
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Pytorch: An imperative style, high-performance deep learning library
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, et al · 2019
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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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Distilbert, a distilled version of bert: smaller, faster, cheaper and lighter
Victor Sanh, Lysandre Debut, Julien Chaumond, and Thomas Wolf · 2019
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Physics-constrained deep learning for high-dimensional surrogate modeling and uncertainty quantification without labeled data
Yinhao Zhu, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis, and Paris Perdikaris · 2019
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An image is worth 16x16 words: Transformers for image recognition at scale
Assessing physics informed neural networks in ocean modelling and climate change applications
Taco de Wolff, Hugo Carrillo, Luis Martí, and Nayat Sanchez-Pi · 2021
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A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
Ehsan Haghighat, Maziar Raissi, Adrian Moure, Hector Gomez, and Ruben Juanes · 2021
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Characterizing possible failure modes in physics-informed neural networks
Aditi Krishnapriyan, Amir Gholami, Shandian Zhe, Robert Kirby, and Michael W Mahoney · 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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Physics-informed neural networks for solving forward and inverse flow problems via the boltzmann-bgk formulation
Qin Lou, Xuhui Meng, and George Em Karniadakis · 2021
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Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, et al · 2020
Cited alongside, same era.
Limitations of physics informed machine learning for nonlinear two-phase transport in porous media
Olga Fuks and Hamdi A Tchelepi · 2020
Cited alongside, same era.
Conformer: Convolution-augmented transformer for speech recognition
Anmol Gulati, James Qin, Chung-Cheng Chiu, Niki Parmar, Yu Zhang, Jiahui Yu, Wei Han, Shibo Wang, Zhengdong Zhang, Yonghui Wu, et al · 2020
Cited alongside, same era.
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Ameya D Jagtap, Kenji Kawaguchi, and George Em Karniadakis · 2020
Cited alongside, same era.
Fourier neural operator for parametric partial differential equations
Zongyi Li, Nikola Kovachki, Kamyar Azizzadenesheli, Burigede Liu, Kaushik Bhattacharya, Andrew Stuart, and Anima Anandkumar · 2020
Cited alongside, same era.
Physics-informed neural networks for high-speed flows
Zhiping Mao, Ameya D Jagtap, and George Em Karniadakis · 2020
Cited alongside, same era.
Self-adaptive physics-informed neural networks using a soft attention mechanism
Levi McClenny and Ulisses Braga-Neto · 2020
Cited alongside, same era.
Physics-informed generative adversarial networks for stochastic differential equations
Liu Yang, Dongkun Zhang, and George Em Karniadakis · 2020
Cited alongside, same era.
Physics-informed neural networks with hard constraints for inverse design
Lu Lu, Raphael Pestourie, Wenjie Yao, Zhicheng Wang, Francesc Verdugo, and Steven G Johnson · 2021
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Understanding and mitigating gradient flow pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, and Paris Perdikaris · 2021
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Informer: Beyond efficient transformer for long sequence time-series forecasting
Haoyi Zhou, Shanghang Zhang, Jieqi Peng, Shuai Zhang, Jianxin Li, Hui Xiong, and Wancai Zhang · 2021
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Rethinking the importance of sampling in physics-informed neural networks
Arka Daw, Jie Bu, Sifan Wang, Paris Perdikaris, and Anuj Karpatne · 2022
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Rambod Mojgani, Maciej Balajewicz, and Pedram Hassanzadeh · 2022
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How do vision transformers work?
Namuk Park and Songkuk Kim · 2022
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A versatile framework to solve the helmholtz equation using physics-informed neural networks
Chao Song, Tariq Alkhalifah, and Umair Bin Waheed · 2022
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Learning in sinusoidal spaces with physics-informed neural networks
Jian Cheng Wong, Chinchun Ooi, Abhishek Gupta, and Yew-Soon Ong · 2022
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Physics informed machine learning with misspecified priors: \ \backslash \ \backslash an analysis of turning operation in lathe machines
Zhiyuan Zhao, Xueying Ding, Gopaljee Atulya, Alex Davis, and Aarti Singh · 2022
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