PREDICTION OF NONDEGENERATE SOLITONS AND PARAMETERS IN NONLINEAR BIREFRINGENT OPTICAL FIBERS USING PHPINN AND DEEPONET ALGORITHMS

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

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

Nature Machine Intelligence · 2021 · 2.8K citations · Full text

Computing, Computer Science, Mathematics +10

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

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

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Sifan Wang, Hanwen Wang, Paris Perdikaris · Science Advances · 2021 · 726 citations · Full text

Computing, Computer Science, Data Science +14