Radial basis function neural network (RBFNN) approximation of Cauchy inverse problems of the Laplace equation

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

On the limited memory BFGS method for large scale optimization

Jorge Nocedal · Mathematical Programming · 1989 · 8.5K citations

Computing, Computer Engineering, Computer Science +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

Monte Carlo and quasi-Monte Carlo methods

Russel E. Caflisch · Acta Numerica · 1998 · 1.7K citations

Natural Sciences, Physics, Computational Fluid Dynamics +13