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Though PINNs (physics-informed neural networks) are now deemed as a complement to traditional CFD (computational fluid dynamics) solvers rather than a replacement, their ability to solve the Navier-Stokes equations without given data is still of great interest.
A numerical method of solving the navier-stokes equations
V.A. Gushchin and V.V. Shchennikov · 1974
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A numerical study of steady viscous flow past a circular cylinder
Bengt Fornberg · 1980
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Hydrodynamic studies on two traveling wavy foils in tandem arrangement
Jian Deng, Xue-Ming Shao, and Zhao-Sheng Yu · 2007
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Numerical simulation of laminar flow past a circular cylinder
B.N. Rajani, A. Kandasamy, and Sekhar Majumdar · 2008
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Vortex Shedding for Flow Past Circular Cylinder: Effects of Initial Conditions
Mouna Laroussi and Mohamed Djebbi · 2015
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PetIBM: toolbox and applications of the immersed-boundary method on distributed-memory architectures
Pi-Yueh Chuang, Olivier Mesnard, Anush Krishnan, and Lorena A. Barba · 2018
Cited alongside, same era.
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 · 2018
Cited alongside, same era.
DGM: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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AI has cracked a key mathematical puzzle for understanding our world
Karen Hao · 2020
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Physics-informed neural networks (PINNs) for fluid mechanics: a review
Shengze Cai, Zhiping Mao, Zhicheng Wang, Minglang Yin, and George Em Karniadakis
Cited in the paper.
Neural-network-based approximations for solving partial differential equations
M. W. M. G. Dissanayake and N. Phan-Thien
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Evolutional deep neural network
Yifan Du and Tamer A. Zaki
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Unsteady fluid mechanics applications of neural networks
William E. Faller and Scott J. Schreck
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Gaussian error linear units (GELUs)
Dan Hendrycks and Kevin Gimpel
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Approximation capabilities of multilayer feedforward networks
Kurt Hornik
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Artificial neural networks for solving ordinary and partial differential equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis
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Numerical solution of elliptic partial differential equation using radial basis function neural networks
Jianyu Li, Siwei Luo, Yingjian Qi, and Yaping Huang
Cited in the paper.
Meshfreeflownet: A physics-constrained deep continuous space-time super-resolution framework
Chiyu “Max” Jiang, Soheil Esmaeilzadeh, Kamyar Azizzadenesheli, Karthik Kashinath, Mustafa Mustafa, Hamdi A. Tchelepi, Philip Marcus, Mr Prabhat, and Anima Anandkumar · 2020
Later among the works it cites.
A novel physics informed deep learning method for simulation-based modelling
Hasan Karali, Umut M. Demirezen, Mahmut A. Yukselen, and Gokhan Inalhan · 2021
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When and why PINNs fail to train: A neural tangent kernel perspective
Sifan Wang, Xinling Yu, and Paris Perdikaris · 2021
Later among the works it cites.
barbagroup/scipy-2022-repro-pack: 20220530, May 2022
Pi-Yueh Chuang · 2022
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