Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves

Multilayer feedforward networks are universal approximators

Kurt Hornik, Maxwell B. Stinchcombe, Halbert White · Neural Networks · 1989 · 21.2K citations

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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, George Em Karniadakis · Journal of Computational Physics · 2018 · 16.9K citations · Full text

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Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations

Maziar Raissi, Alireza Yazdani, George Em Karniadakis · Science · 2020 · 2K citations · Full text

Computing, Computer Science, Physics +16

Physics-informed neural networks for high-speed flows

Zhiping Mao, Ameya D. Jagtap, George Em Karniadakis · Computer Methods in Applied Mechanics and Engineering · 2019 · 1.2K citations

Computing, Computational Engineering, Physics +14

When and why PINNs fail to train: A neural tangent kernel perspective

Sifan Wang, Xinling Yu, Paris Perdikaris · Journal of Computational Physics · 2021 · 1.2K citations · Full text

Computing, Computer Science, Machine Learning +4