On the influence of over-parameterization in manifold based surrogates and deep neural operators

ImageNet classification with deep convolutional neural networks

Alex Krizhevsky, Ilya Sutskever, Geoffrey E. Hinton · Communications of the ACM · 2017 · 75.7K citations · Full text

Computing, Computer Science, Computer Vision +12

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

Scikit-learn: Machine Learning in Python

PedregosaFabian, VaroquauxGaël, GramfortAlexandre et al. · Journal of Machine Learning Research · 2011 · 8.2K citations

Computing, Computer Science, Artificial Intelligence +10

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

Dongbin Xiu, George Em Karniadakis · SIAM Journal on Scientific Computing · 2002 · 4.7K citations

Natural Sciences, Computational Engineering, Mathematics +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