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Supervised operator learning is an emerging machine learning paradigm with applications to modeling the evolution of spatio-temporal dynamical systems and approximating general black-box relationships between functional data.
An algorithm for the machine calculation of complex Fourier series
James W Cooley and John W Tukey · 1965
Earlier work this paper cites.
When the data are functions
James O Ramsay · 1982
Earlier work this paper cites.
Orthogonal bases of compactly supported wavelets, communications on pure and applied, 1988
I Daubechies · 1988
Earlier work this paper cites.
Some tools for functional data analysis
James O Ramsay and CJ Dalzell · 1991
Earlier work this paper cites.
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems
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Earlier work this paper cites.
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Eugenia Kalnay, Masao Kanamitsu, Robert Kistler, William Collins, Dennis Deaven, Lev Gandin, Mark Iredell, Suranjana Saha, Glenn White, John Woollen, et al · 1996
Earlier work this paper cites.
Kernel methods for pattern analysis
John Shawe-Taylor, Nello Cristianini, et al · 2004
Earlier work this paper cites.
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Charles A Micchelli and Massimiliano Pontil · 2004
Earlier work this paper cites.
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Random features for large-scale kernel machines
Ali Rahimi, Benjamin Recht, et al · 2007
Earlier work this paper cites.
Matplotlib: A 2D graphics environment
John D Hunter · 2007
Earlier work this paper cites.
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Thomas Hofmann, Bernhard Schölkopf, and Alexander J Smola · 2008
Earlier work this paper cites.
Universal multi-task kernels
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Earlier work this paper cites.
The elements of statistical learning: data mining, inference, and prediction
Trevor Hastie, Robert Tibshirani, and Jerome Friedman · 2009
Earlier work this paper cites.
Nonlinear functional regression: a functional RKHS approach
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Earlier work this paper cites.
Understanding the difficulty of training deep feedforward neural networks
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Earlier work this paper cites.
Universal kernels on non-standard input spaces
Andreas Christmann and Ingo Steinwart · 2010
Earlier work this paper cites.
Universality, characteristic kernels and RKHS embedding of measures
Bharath K. Sriperumbudur, Kenji Fukumizu, and Gert R.G. Lanckriet · 2011
Earlier work this paper cites.
Group invariant scattering
Stéphane Mallat · 2012
Earlier work this paper cites.
Invariant scattering convolution networks
Joan Bruna and Stéphane Mallat · 2013
Earlier work this paper cites.
Dynamics of fluids in porous media
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Earlier work this paper cites.
Adam: A method for stochastic optimization
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Earlier work this paper cites.
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