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Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling.
Liii. on lines and planes of closest fit to systems of points in space
Karl Pearson · 1901
Earlier work this paper cites.
Turbulence and the dynamics of coherent structures. i. coherent structures
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Numerical methods for shallow-water flow
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Earlier work this paper cites.
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Earlier work this paper cites.
A global geometric framework for nonlinear dimensionality reduction
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Earlier work this paper cites.
Proper orthogonal decomposition and its applications—Part I: Theory
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Earlier work this paper cites.
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Earlier work this paper cites.
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Earlier work this paper cites.
Model order reduction: theory, research aspects and applications
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Earlier work this paper cites.
Dimensionality reduction: A comparative review
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Earlier work this paper cites.
Fundamentals of engineering numerical analysis
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Earlier work this paper cites.
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Earlier work this paper cites.
Auto-Encoding Variational Bayes
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