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20192021
most citedVariational Physics-Informed Neural Networks For Solving Partial Differential Equations

199 citations · 201 across the 3 of their papers we have counts for

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cs.NE2020

hp-VPINNs: Variational Physics-Informed Neural Networks With Domain Decomposition

Ehsan Kharazmi, Zhongqiang Zhang, George Em Karniadakis

We formulate a general framework for hp-variational physics-informed neural networks (hp-VPINNs) based on the nonlinear approximation of shallow and deep neural networks and hp-ref…

cs.NE2019★ 199 cited

Variational Physics-Informed Neural Networks For Solving Partial Differential Equations

E. Kharazmi, Z. Zhang, G. E. Karniadakis

Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random se…