Probabilistic learning on manifolds
The probabilistic learning on manifolds (PLoM)[1] is a novel type machine learning technique to construct learned datasets from a given small dataset.
Originally proposed by Christian Soize and Roger Ghanem in 2016,[2] the methodology has been gaining ground in several machine learning applications[3] in computational science and engineering, especially in inverse problems, optimization, and uncertainty quantification, where it is often necessary to evaluate an extremely costly function defined by a computational model. In this context, initially, the expensive computational model is used to generate a small initial dataset, which is used in the learning process of the PLoM technique, which therefore generates (in a cheap way) a large secondary dataset whose distribution emulates the baseline dataset distribution.
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