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Software_PLoM_with_partition_2021_06_24

Abstract : 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 SIAM-ASA Journal on Uncertainty Quantification}, 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 Numerical 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 SIAM-ASA Journal on Uncertainty Quantification, 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"
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Contributor : Christian Soize <>
Submitted on : Wednesday, June 30, 2021 - 4:36:59 PM
Last modification on : Thursday, July 8, 2021 - 3:30:05 AM

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Christian Soize. Software_PLoM_with_partition_2021_06_24. 2021. ⟨hal-03275052⟩

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