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This PLoM (Probabilistic Learning on Manifolds) software is a novel version of the PLoM algorithm for which the first version of the algorithm was published in Ref. [1] and for which the mathematics foundations can be found in Ref. [2]. The present version of this PLoM software includes three novel capabilities: - parallel computing - automatic indentification of the smoothing parameter of the DMAP kernel as explained in Ref. [3]. - possibility to introduce constraints for keeping the normalization of the PCA coordinates during the probabilistic learning process as explained in Ref. [3], based on Ref. [4]. The input data parameters entered for each STEP correpond to those for Application 1 for which the results are in the file: "listing_RESULTS.txt" Publications: [1] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, doi:10.1016/, 321, 242-258 (2016). [2] C. Soize, R. Ghanem, Probabilistic learning on manifolds, Foundations of Data Science, American Institute of Mathematical Sciences (AIMS), doi: 10.3934/fods.2020013, 2(3), 279-307 (2020). Also in arXiv:2002.12653 [math.ST], 28 Feb 2020, [3] C. Soize, R. Ghanem, Probabilistic learning on manifolds with partition, in arXiv:2010.14324 [stat.ML], 21 Feb 2021, Also submitted in SIAM-ASA Journal on Uncertainty Quantification}, 2021. [ [4] C. Soize, R. Ghanem, Physics-constrained non-Gaussian probabilistic learning on manifolds, International Journal for Numerical Methods in Engineering, doi: 10.1002/nme.6202, 121 (1), 110-145 (2020).

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hal-03274618 , version 1 (30-06-2021)


  • HAL Id : hal-03274618 , version 1


Christian Soize. Software_PLoM_2021_02_21. 2021. ⟨hal-03274618⟩
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