Transferable Neural Networks for Partial Differential Equations

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

Approximation by superpositions of a sigmoidal function

George Cybenko · Mathematics of Control Signals and Systems · 1989 · 13.7K citations

Computing, Computer Science, Machine Learning +5

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

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