Software_PLoM_with_partition_2021_06_24

The software "Probabilisting Learning on Manifolds (PLoM) with Partition" is a novel version of the PLoM 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 with partition is based on Ref.[3] and includes four novel capabilities: - probabilistic learning on manifolds with partition that consists (i) in computing, before the learning, an optimal partition in terms of independent random vectors (groups) using the algorithm presented Ref.[4] and (ii) in performing the probabilistic learning for each group of the identified partition. - parallel computing. - automatic identification of the smoothing parameter of the DMAP kernel as explained in Ref.[3]. - possibility to introduce constraints for preserving the normalization of the PCA coordinates during probabilistic learning process as explained in Ref.[3], based on Ref.[5]. 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 International Journal for Numerical Methods in Engineering, 2021. [4] C. Soize, Optimal partition in terms of independent random vectors of any non-Gaussian vector defined by a set of realizations, SIAM-ASA Journal on Uncertainty Quantification, doi: 10.1137/16M1062223, 5(1), 176-211 (2017). [5] C. Soize, R. Ghanem, Physics-constrained non-Gaussian probabilistic learning on manifolds, International Journal for Methods in Engineering, doi: 10.1002/nme.6202, 121 (1), 110-145 (2020). This version allows for reproducing Application 1 of the paper: [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 International Journal for Numerical Methods in Engineering, 2021". The input data parameters entered for each STEP correpond to those for Application AP1 for which the results are in the directory "Results_AP1