Software_PLoM_2021_02_21
Abstract
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/j.jcp.2016.05.044, 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, https://arxiv.org/abs/2002.12653.
[3] C. Soize, R. Ghanem, Probabilistic learning on manifolds with partition, in arXiv:2010.14324 [stat.ML], 21 Feb 2021,
https://arxiv.org/abs/2102.10894.
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).