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Probabilistic learning on manifolds
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The probabilistic learning on manifolds (PLoM) 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, the methodology has been gaining ground in several machine learning applications 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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