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Physics-Informed Neural Networks (PINNs) are a class of deep learning neural networks that learn the response of a physical system without any simulation data, and only by incorporating the governing partial differential equations (PDEs) in their loss function.
“Approximate distance fields with non-vanishing gradients”
Arpan Biswas and Vadim Shapiro · 2004
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Paulius Micikevicius et al · 2017
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“Automatic differentiation in machine learning: a survey”
Atilim Baydin, Barak Pearlmutter, Alexey Radul and Jeffrey Siskind · 2018
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“PDE-Net 2.0: Learning PDEs from data with a numeric-symbolic hybrid deep network”
Zichao Long, Yiping Lu and Bin Dong · 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 Karniadakis · 2019
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“Physics-informed neural networks for inverse problems in nano-optics and metamaterials”
Yuyao Chen, Lu Lu, George Karniadakis and Luca Dal · 2020
Earlier work this paper cites.
“Modeling the dynamics of PDE systems with physics-constrained deep auto-regressive networks”
Nicholas Geneva and Nicholas Zabaras · 2020
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“Learning mesh-based simulation with graph networks”
Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez and Peter Battaglia · 2020
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“Deep neural networks motivated by partial differential equations”
Lars Ruthotto and Eldad Haber · 2020
Earlier work this paper cites.
“A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs”
Stefania Fresca, Luca Dede and Andrea Manzoni · 2021
Cited alongside, same era.
“PhyGeoNet: Physics-informed geometry-adaptive convolutional neural networks for solving parameterized steady-state PDEs on irregular domain”
Han Gao, Luning Sun and Jian-Xun Wang · 2021
Cited alongside, same era.
“Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems”
Han Gao, Matthew. Zahr and Jian-Xun Wang · 2021
Cited alongside, same era.
“NVIDIA SimNet™: An AI-accelerated multi-physics simulation framework”
Oliver Hennigh et al · 2021
Cited alongside, same era.
“Physics-informed neural networks for solving forward and inverse flow problems via the Boltzmann-BGK formulation”
Qin Lou, Xuhui Meng and George Karniadakis · 2021
Cited alongside, same era.
“B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data”
Liu Yang, Xuhui Meng and George Karniadakis · 2021
Later among the works it cites.
“Physics-informed neural networks (PINNs) for fluid mechanics: A review”
Shengze Cai et al · 2022
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“Scientific machine learning through physics–informed neural networks: Where we are and what’s next”
Salvatore Cuomo et al · 2022
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Meire Fortunato et al · 2022
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“A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations”
Revanth Mattey and Susanta Ghosh · 2022
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“Efficient training of physics-informed neural networks via importance sampling”
Mohammad Nabian, Rini Gladstone and Hadi Meidani · 2021
Cited alongside, same era.
“Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks”
N. Sukumar and Ankit Srivastava · 2021
Cited alongside, same era.
“Physics-based Deep Learning”
Nils Thuerey et al · 2021
Cited alongside, same era.
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Khang Luong, Thang Le-Duc and Jaehong Lee · 2023
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