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Variational Physics-Informed Neural Networks (VPINNs) utilize a variational loss function to solve partial differential equations, mirroring Finite Element Analysis techniques.
Artificial neural networks for solving ordinary and partial differential equations
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ParMooN—a modernized program package based on mapped finite elements
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Workshop report on basic research needs for scientific machine learning: Core technologies for artificial intelligence
N. Baker, F. Alexander, T. Bremer, A. Hagberg, Y. Kevrekidis, H. Najm, M. Parashar, A. Patra, J. Sethian, S. Wild, K. Willcox, and S. Lee · 2019
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Variational physics-informed neural networks for solving partial differential equations
E. Kharazmi, Z. Zhang, and G. E. Karniadakis · 2019
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2019
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Towards understanding the spectral bias of deep learning, 2020
Y. Cao, Z. Fang, Y. Wu, D.-X. Zhou, and Q. Gu · 2020
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SParSH-AMG: A library for hybrid CPU-GPU algebraic multigrid and preconditioned iterative methods
S. Ganesan and M. Shah · 2020
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Varnet: Variational neural networks for the solution of partial differential equations
R. Khodayi-Mehr and M. Zavlanos · 2020
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Physics-informed neural networks for high-speed flows
Z. Mao, A. D. Jagtap, and G. E. Karniadakis · 2020
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Meshless physics-informed deep learning method for three-dimensional solid mechanics
D. W. Abueidda, Q. Lu, and S. Koric · 2021
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Physics-informed neural networks (PINNs) for fluid mechanics: A review
Scientific machine learning through physics–informed neural networks: Where we are and what’s next
S. Cuomo, V. S. Di Cola, F. Giampaolo, G. Rozza, M. Raissi, and F. Piccialli · 2022
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Physics-informed neural networks for solving Reynolds-averaged Navier–Stokes equations
H. Eivazi, M. Tahani, P. Schlatter, and R. Vinuesa · 2022
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Analyses of internal structures and defects in materials using physics-informed neural networks
E. Zhang, M. Dao, G. E. Karniadakis, and S. Suresh · 2022
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hp-VPINNs: High-performance variational physics-informed neural networks, 2023
E. Kharazmi · 2023
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cv-PINN: Efficient learning of variational physics-informed neural network with domain decomposition
C. Liu and H. Wu · 2023
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S. Cai, Z. Mao, Z. Wang, M. Yin, and G. E. Karniadakis · 2021
Cited alongside, same era.
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
E. Haghighat, M. Raissi, A. Moure, H. Gomez, and R. Juanes · 2021
Cited alongside, same era.
hp-VPINNs: Variational physics-informed neural networks with domain decomposition
E. Kharazmi, Z. Zhang, and G. E. Karniadakis · 2021
Cited alongside, same era.
HypoSVI: Hypocentre inversion with Stein variational inference and physics informed neural networks
J. D. Smith, Z. E. Ross, K. Azizzadenesheli, and J. B. Muir · 2021
Cited alongside, same era.
hp-Variational Physics-Informed Neural Networks for Nonlinear Two-Phase Transport in Porous Media
M. Yang and J. T. Foster · 2021
Cited alongside, same era.
DeepXDE: A deep learning library for solving differential equations
L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis
Cited in the paper.
Physics-informed neural networks with hard constraints for inverse design
L. Lu, R. Pestourie, W. Yao, Z. Wang, F. Verdugo, and S. G. Johnson
Cited in the paper.
NVIDIA · 2023
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Uncertainty quantification in scientific machine learning: Methods, metrics, and comparisons
A. F. Psaros, X. Meng, Z. Zou, L. Guo, and G. E. Karniadakis · 2023
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Effects of variational formulations on physics-informed neural network performance in solid mechanics
N. Radin, S. Klinkel, and O. Altay · 2023
Later among the works it cites.
https://developer.nvidia.com/modulus . Last accessed Jan 01, 2024
NVIDIA Modulus · 2024
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