Boussinesq equation solved by the physics-informed neural networks

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

Natural Sciences, Computer Science, Physics +16

Linear and Nonlinear Waves

K. J. Whiteman · Physics Bulletin · 1975 · 7.1K citations

Natural Sciences, Mathematics, Physics +12

Artificial neural networks for solving ordinary and partial differential equations

IEEE Transactions on Neural Networks · 1998 · 2.2K citations · Full text

Natural Sciences, Computational Engineering, Computer Science +17

DGM: A deep learning algorithm for solving partial differential equations

Justin Sirignano, Konstantinos Spiliopoulos · Journal of Computational Physics · 2018 · 2.1K citations · Full text

Natural Sciences, Computer Science, Mathematics +13

Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks

Sifan Wang, Yujun Teng, Paris Perdikaris · SIAM Journal on Scientific Computing · 2021 · 1.6K citations

Natural Sciences, Computer Science, Physics +14