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Physics-informed neural networks (PINNs) have been popularized as a deep learning framework that can seamlessly synthesize observational data and partial differential equation (PDE) constraints.
High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method
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Neural tangent kernel: Convergence and generalization in neural networks
Arthur Jacot, Franck Gabriel, and Clément Hongler · 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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Deep physical informed neural networks for metamaterial design
Zhiwei Fang and Justin Zhan · 2019
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On the spectral bias of neural networks
Nasim Rahaman, Aristide Baratin, Devansh Arpit, Felix Draxler, Min Lin, Fred Hamprecht, Yoshua Bengio, and Aaron Courville · 2019
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Frequency principle: Fourier analysis sheds light on deep neural networks
Zhi-Qin John Xu, Yaoyu Zhang, Tao Luo, Yanyang Xiao, and Zheng Ma · 2019
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Towards understanding the spectral bias of deep learning
Yuan Cao, Zhiying Fang, Yue Wu, Ding-Xuan Zhou, and Quanquan Gu · 2019
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The convergence rate of neural networks for learned functions of different frequencies
Basri Ronen, David Jacobs, Yoni Kasten, and Shira Kritchman · 2019
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On exact computation with an infinitely wide neural net
Sanjeev Arora, Simon S Du, Wei Hu, Zhiyuan Li, Russ R Salakhutdinov, and Ruosong Wang · 2019
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Wide neural networks of any depth evolve as linear models under gradient descent
Jaehoon Lee, Lechao Xiao, Samuel Schoenholz, Yasaman Bahri, Roman Novak, Jascha Sohl-Dickstein, and Jeffrey Pennington · 2019
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Natural language processing
KR1442 Chowdhary and KR Chowdhary · 2020
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Ab-initio solution of the many-electron schrödinger equation with deep neural networks
D. Pfau, J.S. Spencer, A.G. de G. Matthews, and W.M.C. Foulkes · 2020
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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Maziar Raissi, Alireza Yazdani, and George Em Karniadakis · 2020
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Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data
Luning Sun, Han Gao, Shaowu Pan, and Jian-Xun Wang · 2020
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Physics-informed neural networks for cardiac activation mapping
Francisco Sahli Costabal, Yibo Yang, Paris Perdikaris, Daniel E Hurtado, and Ellen Kuhl · 2020
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Machine learning in cardiovascular flows modeling: Predicting arterial blood pressure from non-invasive 4D flow MRI data using physics-informed neural networks
Georgios Kissas, Yibo Yang, Eileen Hwuang, Walter R Witschey, John A Detre, and Paris Perdikaris · 2020
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Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Yuyao Chen, Lu Lu, George Em Karniadakis, and Luca Dal Negro · 2020
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Nvidia simnetˆ { \{ TM } \} : an ai-accelerated multi-physics simulation framework
Oliver Hennigh, Susheela Narasimhan, Mohammad Amin Nabian, Akshay Subramaniam, Kaustubh Tangsali, Max Rietmann, Jose del Aguila Ferrandis, Wonmin Byeon, Zhiwei Fang, and Sanjay Choudhry · 2020
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Self-adaptive physics-informed neural networks using a soft attention mechanism
Sobolev training for physics informed neural networks
Hwijae Son, Jin Woo Jang, Woo Jin Han, and Hyung Ju Hwang · 2021
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Characterizing possible failure modes in physics-informed neural networks
Aditi S Krishnapriyan, Amir Gholami, Shandian Zhe, Robert M Kirby, and Michael W Mahoney · 2021
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One-shot transfer learning of physics-informed neural networks
Shaan Desai, Marios Mattheakis, Hayden Joy, Pavlos Protopapas, and Stephen Roberts · 2021
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Transfer learning based multi-fidelity physics informed deep neural network
Souvik Chakraborty · 2021
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A method for representing periodic functions and enforcing exactly periodic boundary conditions with deep neural networks
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Levi McClenny and Ulisses Braga-Neto · 2020
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Ameya D Jagtap, Kenji Kawaguchi, and George Em Karniadakis · 2020
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Ziqi Liu, Wei Cai, and Zhi-Qin John Xu · 2020
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Implicit neural representations with periodic activation functions
Vincent Sitzmann, Julien Martel, Alexander Bergman, David Lindell, and Gordon Wetzstein · 2020
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Solving Allen-Cahn and Cahn-Hilliard equations using the adaptive physics informed neural networks
Colby L Wight and Jia Zhao · 2020
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Transfer learning enhanced physics informed neural network for phase-field modeling of fracture
Somdatta Goswami, Cosmin Anitescu, Souvik Chakraborty, and Timon Rabczuk · 2020
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Frequency bias in neural networks for input of non-uniform density
Ronen Basri, Meirav Galun, Amnon Geifman, David Jacobs, Yoni Kasten, and Shira Kritchman · 2020
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Fourier features let networks learn high frequency functions in low dimensional domains
Matthew Tancik, Pratul P Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan T Barron, and Ren Ng · 2020
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Suchuan Dong and Naxian Ni · 2021
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N Sukumar and Ankit Srivastava · 2021
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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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Machine learning–accelerated computational fluid dynamics
Dmitrii Kochkov, Jamie A. Smith, Ayya Alieva, Qing Wang, Michael P. Brenner, and Stephan Hoyer · 2021
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Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopadhyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, et al · 2022
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Graphcast: Learning skillful medium-range global weather forecasting
Remi Lam, Alvaro Sanchez-Gonzalez, Matthew Willson, Peter Wirnsberger, Meire Fortunato, Alexander Pritzel, Suman Ravuri, Timo Ewalds, Ferran Alet, Zach Eaton-Rosen, et al · 2022
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Analyses of internal structures and defects in materials using physics-informed neural networks
Enrui Zhang, Ming Dao, George Em Karniadakis, and Subra Suresh · 2022
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Conditional physics informed neural networks
Alexander Kovacs, Lukas Exl, Alexander Kornell, Johann Fischbacher, Markus Hovorka, Markus Gusenbauer, Leoni Breth, Harald Oezelt, Masao Yano, Noritsugu Sakuma, et al · 2022
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Hyposvi: Hypocentre inversion with stein variational inference and physics informed neural networks
Jonthan D Smith, Zachary E Ross, Kamyar Azizzadenesheli, and Jack B Muir · 2022
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When and why PINNs fail to train: A neural tangent kernel perspective
Sifan Wang, Xinling Yu, and Paris Perdikaris · 2022
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Inverse dirichlet weighting enables reliable training of physics informed neural networks
Suryanarayana Maddu, Dominik Sturm, Christian L Müller, and Ivo F Sbalzarini · 2022
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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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Pixel: Physics-informed cell representations for fast and accurate pde solvers
Namgyu Kang, Byeonghyeon Lee, Youngjoon Hong, Seok-Bae Yun, and Eunbyung Park · 2022
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Is l 2 l^{2} physics informed loss always suitable for training physics informed neural network?
Chuwei Wang, Shanda Li, Di He, and Liwei Wang · 2022
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Can-pinn: A fast physics-informed neural network based on coupled-automatic–numerical differentiation method
Pao-Hsiung Chiu, Jian Cheng Wong, Chinchun Ooi, My Ha Dao, and Yew-Soon Ong · 2022
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Thermodynamically consistent physics-informed neural networks for hyperbolic systems
Ravi G Patel, Indu Manickam, Nathaniel A Trask, Mitchell A Wood, Myoungkyu Lee, Ignacio Tomas, and Eric C Cyr · 2022
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Gradient-enhanced physics-informed neural networks for forward and inverse pde problems
Jeremy Yu, Lu Lu, Xuhui Meng, and George Em Karniadakis · 2022
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Respecting causality is all you need for training physics-informed neural networks
Sifan Wang, Shyam Sankaran, and Paris Perdikaris · 2022
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Random weight factorization improves the training of continuous neural representations
Sifan Wang, Hanwen Wang, Jacob H Seidman, and Paris Perdikaris · 2022
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Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration
Pi-Yueh Chuang and Lorena A Barba · 2022
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Climax: A foundation model for weather and climate
Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K Gupta, and Aditya Grover · 2023
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A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks
Chenxi Wu, Min Zhu, Qinyang Tan, Yadhu Kartha, and Lu Lu · 2023
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