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While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date, PINNs have not been successful in simulating multi-scale and singular perturbation problems.
Popular ensemble methods: An empirical study
David Opitz and Richard Maclin · 1999
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Stochastic gradient boosting
Jerome H Friedman · 2002
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Robust dpg method for convection-dominated diffusion problems
Leszek Demkowicz and Norbert Heuer · 2013
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Deep hidden physics models: Deep learning of nonlinear partial differential equations
Maziar Raissi · 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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Limitations of physics informed machine learning for nonlinear two-phase transport in porous media
Olga Fuks and Hamdi A Tchelepi · 2020
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Extended physics-informed neural networks (xpinns): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
Ameya D Jagtap and George Em Karniadakis · 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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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations
Maziar Raissi, Alireza Yazdani, and George Em Karniadakis · 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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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
Cited alongside, same era.
Fourier features let networks learn high frequency functions in low dimensional domains
Matthew Tancik, Pratul Srinivasan, Ben Mildenhall, Sara Fridovich-Keil, Nithin Raghavan, Utkarsh Singhal, Ravi Ramamoorthi, Jonathan Barron, and Ren Ng · 2020
Nvidia simnet™: An ai-accelerated multi-physics simulation framework
Oliver Hennigh, Susheela Narasimhan, Mohammad Amin Nabian, Akshay Subramaniam, Kaustubh Tangsali, Zhiwei Fang, Max Rietmann, Wonmin Byeon, and Sanjay Choudhry · 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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Understanding and mitigating gradient flow pathologies in physics-informed neural networks
Sifan Wang, Yujun Teng, and Paris Perdikaris · 2021
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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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Theory-guided physics-informed neural networks for boundary layer problems with singular perturbation
Amirhossein Arzani, Kevin W Cassel, and Roshan M D’Souza · 2023
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Cited alongside, same era.
A gradient boosting method to improve travel time prediction
Yanru Zhang and Ali Haghani · 2020
Cited alongside, same era.
On collocation points for physics-informed neural networks applied to convection-dominated convection-diffusion problems
Derk Frerichs-Mihov, Marwa Zainelabdeen, and Volker John
Cited in the paper.
Jiaxin Deng, Xi’an Li, Jinran Wu, Shaotong Zhang, Weide Li, and You-Gan Wang · 2023
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