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Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Subhayan De, Matthew Reynolds, Malik Hassanaly, Ryan King, Alireza Doostan

Computational Mechanics · 2023 · 38 citations · 31 references

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31

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

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The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations

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

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Bayesian Calibration of Computer Models

Marc C. Kennedy, Anthony O’Hagan · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 2001 · 4.2K citations · Full text

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

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

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Turbulence Modeling in the Age of Data

Karthik Duraisamy, Gianluca Iaccarino, Heng Xiao · Annual Review of Fluid Mechanics · 2018 · 1.4K citations · Full text

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