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Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering.
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Multifidelity uncertainty quantification using non-intrusive polynomial chaos and stochastic collocation
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Group equivariant convolutional networks
Taco Cohen and Max Welling · 2016
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Samuel H Rudy, Steven L Brunton, Joshua L Proctor, and J Nathan Kutz · 2017
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Decoupled weight decay regularization
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Nonlinear information fusion algorithms for data-efficient multi-fidelity modelling
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Similarity solutions to burgers’ equation in terms of special functions of mathematical physics
Turgut Öziş and İSMAİL Aslan · 2017
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Large batch training of convolutional networks
Yang You, Igor Gitman, and Boris Ginsburg · 2017
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Mazier Raissi, Paris Perdikaris, and George E. Karniadakis · 2018
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Deep learning for universal linear embeddings of nonlinear dynamics
Bethany Lusch, J Nathan Kutz, and Steven L Brunton · 2018
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Representation learning with contrastive predictive coding
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Deep clustering for unsupervised learning
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Learning data-driven discretizations for partial differential equations
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