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Physics-informed neural networks (PINNs) have lately received great attention thanks to their flexibility in tackling a wide range of forward and inverse problems involving partial differential equations.
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Parviz Moin · 2010
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Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
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Diederik P Kingma and Jimmy Ba · 2014
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Deep neural networks as gaussian processes
Jaehoon Lee, Yasaman Bahri, Roman Novak, Samuel S Schoenholz, Jeffrey Pennington, and Jascha Sohl-Dickstein · 2017
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Physics-informed deep generative models
Yibo Yang and Paris Perdikaris · 2018
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Dgm: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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Solving high-dimensional partial differential equations using deep learning
Jiequn Han, Arnulf Jentzen, and E Weinan · 2018
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Learning parameters and constitutive relationships with physics informed deep neural networks
Alexandre M Tartakovsky, Carlos Ortiz Marrero, Paris Perdikaris, Guzel D Tartakovsky, and David Barajas-Solano · 2018
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Deep hidden physics models: Deep learning of nonlinear partial differential equations
Maziar Raissi · 2018
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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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Gaussian process behaviour in wide deep neural networks
Alexander G de G Matthews, Mark Rowland, Jiri Hron, Richard E Turner, and Zoubin Ghahramani · 2018
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Deep learning of turbulent scalar mixing
Maziar Raissi, Hessam Babaee, and Peyman Givi · 2019
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Deep learning of vortex-induced vibrations
Maziar Raissi, Zhicheng Wang, Michael S Triantafyllou, and George Em Karniadakis · 2019
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Deep physical informed neural networks for metamaterial design
Zhiwei Fang and Justin Zhan · 2019
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Multi-fidelity physics-constrained neural network and its application in materials modeling
Dehao Liu and Yan Wang · 2019
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Adversarial uncertainty quantification in physics-informed neural networks
Yibo Yang and Paris Perdikaris · 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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fpinns: Fractional physics-informed neural networks
Guofei Pang, Lu Lu, and George Em Karniadakis · 2019
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Lu Lu, Pengzhan Jin, and George Em Karniadakis · 2019
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Xiaowei Jin, Shengze Cai, Hui Li, 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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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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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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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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Learning in modal space: Solving time-dependent stochastic PDEs using physics-informed neural networks
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Physics-informed deep neural networks for learning parameters and constitutive relationships in subsurface flow problems
AM Tartakovsky, C Ortiz Marrero, Paris Perdikaris, GD Tartakovsky, and D Barajas-Solano · 2020
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On the convergence and generalization of physics informed neural networks
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Limitations of physics informed machine learning for nonlinear two-phase transport in porous media
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Understanding and mitigating gradient pathologies in physics-informed neural networks
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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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Frequency bias in neural networks for input of non-uniform density
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