Statistics in Function Space

By D. D. Kosambi. 2016

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A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems (2015, unknown): “POD was introduced for the analysis of turbulent flows by Lumley [162] and is closely related to methods used in other fields such as Karhunen–Loève expansions in stochastic process modeling [160, 142], principal component analysis in statistical analysis [132, 136], and empirical orthogonal eigenfu”
Projection-based model reduction: Formulations for physics-based machine learning (2019, methodology): “sions in stochastic process modeling [65, 66], principal component analysis in statistical analysis [67], and empirical orthogonal eigenfunctions in atmospheric modeling [68].”
Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders (2020, methodology): “ations may be available, but little knowledge of the governing equations exist. 2. Proper orthogonal decomposition In this section, we review the POD technique for the construction of a reduced basis [44, 45]. The interested reader may also nd an excellent ex3 planation of POD and its relationship w”