440 research outputs found
Software PLoM (Probabilistic Learning on Manifolds) with physics constraints 2019_02_07
No full textSoftwares PLoM (Probabilistic Learning on Manifolds) with Physics ConstraintsSource in Matlab2018aThis software allows for reproducing the results of Application (AP1) of the article:"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)"
Software PLoM (Probabilistic Learning on Manifolds) with physics constraints 2019_02_07
No full textSoftwares PLoM (Probabilistic Learning on Manifolds) with Physics ConstraintsSource in Matlab2018aThis software allows for reproducing the results of Application (AP1) of the article:"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)"
Potentially useful probabilistic approaches to uncertainty quantification and statistical surrogate models for metamaterials design
No full textInternational audienceThree aspects will be concerning uncertainty quantification and probabilistic learning [1]. First, as a parametric probabilistic approach to uncertainties, a random field theory with symmetry classes will be presented for modeling heterogeneous elastic media [2,3], with an illustration devoted to stochastic continuum modeling of random interphases derived from atomistic simulations of a polymer nanocomposite, coupled with a statistical inverse problem [4]. Second, as a nonparametric probabilistic approach to uncertainties induced by model-form errors, a nonlinear random operator construction [5] will be presented, with an illustration devoted to the nonlinear dynamics of a micro accelerometer. Finally, the construction of statistical surrogate models for uncertain systems will be addressed using probabilistic learning on manifolds for cases involving small training datasets [6,7], with an illustration focused on concurrent meso-to-macro scale modeling of nonlinear random materials without scale separation [8].[1] C. Soize, An overview on uncertainty quantification and probabilistic learning on manifolds in multiscale mechanics of materials, Mathematics and Mechanics of Complex Systems, 11(1), 87-174 (2023).[2] C. Soize, Non Gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators, Comput. Methods Appl. Mech. Eng., 195(1-3), 26-64 (2006).[3] J. Guilleminot, C. Soize, Stochastic model and generator for random fields with symmetry properties: application to the mesoscopic modeling of elastic random media, Multiscale Modeling and Simulation (A SIAM Interdisciplinary Journal), 11(3), 840-870 (2013). [4] T.T. Le, J. Guilleminot, C. Soize, Stochastic continuum modeling of random interphases from atomistic simulations. Application to a polymer nanocomposite, Comput. Methods Appl. Mech. Eng., 303, 430-449 (2016)[5] C. Soize, C. Farhat, A nonparametric probabilistic approach for quantifying uncertainties in low- and high-dimensional nonlinear models, Int. J. Numer. Methods Eng., 109(6), 837-888 (2017).[6] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, 321, 242-258 (2016).[7] C. Soize, R. Ghanem, Probabilistic-learning-based stochastic surrogate model from small incomplete datasets for nonlinear dynamical systems, Comput. Methods Appl. Mech. Eng., 418, 116498, (2024).[8] P. Chen, J. Guilleminot, C. Soize, Concurrent multiscale simulations of nonlinear random materials using probabilistic learning, Comput. Methods Appl. Mech. Eng., 422, 116837 (2024)
Software_PLoM_2021_02_21
No full textThis 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)
Software_PLoM_2021_02_21
No full textThis 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)
Software_PLoM_with_partition_2021_06_24
No full textThe 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
Software_PLoM_with_partition_2021_06_24
No full textThe 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
A probabilistic learning on manifolds as a new tool in machine learning and data science with applications in computational mechanics
No full textPlenary LectureInternational audienceIn Machine Learning (generally devoted to big-data case), the predictive learning (or the supervised learning) approach consists in identifying/learning a random mapping F: w↦ q = F(w), in which the parameters vector w (input) is modelled by a random vector W with known probability distribution Pw(dw) and where the vector of quantities of interest q (outputs) is the non-Gaussian random variable Q = F(W) = f(W,U) whose probability distribution is unknown, given an initial dataset (or training set) DN = {(wj,qj), j=1,…N} of N independent realizations of random vector (W,Q). The measurable mapping f is deterministic and U is a random vector whose probability distribution is known. The approach of probabilistic learning on manifold (recently introduced) will be presented, which allows for constructing a generator of an estimation of the joint probability distribution PW,Q(dw,dq; N) using only DN, which completely characterizes random mapping F. In this framework, novel computational statistical tools will be presented for the small-data challenge for which N is relatively small and consequently, is not sufficient large for constructing converged statistical estimates. In particular, we will present (1) the identification of the optimal independent component partition of the non-Gaussian random vector, (2) the learning from DN for which additional information is available based either on a nonparametric Bayesian approach or on Information Theory. Several applications will be presented such as, the identification of non-Gaussian random fields for random media, the Bayes inference with probabilistic learning, the robust design of an implant in a biological tissue at mesoscale, the nonparametric model-form uncertainties (i) in nonlinear solid dynamics applied a to MEMS and (ii) in nonlinear computational fluid dynamics applied to a Scramjet, nonconvex optimization under uncertainties. [1] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, 321, 242-258 (2016).[2] 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, 5(1), 176-211 (2017).[3] R. Ghanem, C. Soize, Probabilistic nonconvex constrained optimization with fixed number of function evaluations, International Journal for Numerical Methods in Engineering, 113(4), 719-741 (2018).[4] C. Soize, Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm, Computational Mechanics, 62(3), 477-497 (2018).[5] C. Soize, C. Farhat, Probabilistic learning for model-form uncertainties in nonlinear computational mechanics, International Journal for Numerical Methods in Engineering, Accepted 24 October 2018.[6] C. Soize, R. Ghanem, C. Safta, X. Huan, Z.P. Vane, J. Oefelein, G. Lacaze, H.N. Najm, Enhancing model predictability for a scramjet using probabilistic learning on manifold, AIAA Journal, Accepted 13 September 2018
A probabilistic learning on manifolds as a new tool in machine learning and data science with applications in computational mechanics
No full textPlenary LectureInternational audienceIn Machine Learning (generally devoted to big-data case), the predictive learning (or the supervised learning) approach consists in identifying/learning a random mapping F: w↦ q = F(w), in which the parameters vector w (input) is modelled by a random vector W with known probability distribution Pw(dw) and where the vector of quantities of interest q (outputs) is the non-Gaussian random variable Q = F(W) = f(W,U) whose probability distribution is unknown, given an initial dataset (or training set) DN = {(wj,qj), j=1,…N} of N independent realizations of random vector (W,Q). The measurable mapping f is deterministic and U is a random vector whose probability distribution is known. The approach of probabilistic learning on manifold (recently introduced) will be presented, which allows for constructing a generator of an estimation of the joint probability distribution PW,Q(dw,dq; N) using only DN, which completely characterizes random mapping F. In this framework, novel computational statistical tools will be presented for the small-data challenge for which N is relatively small and consequently, is not sufficient large for constructing converged statistical estimates. In particular, we will present (1) the identification of the optimal independent component partition of the non-Gaussian random vector, (2) the learning from DN for which additional information is available based either on a nonparametric Bayesian approach or on Information Theory. Several applications will be presented such as, the identification of non-Gaussian random fields for random media, the Bayes inference with probabilistic learning, the robust design of an implant in a biological tissue at mesoscale, the nonparametric model-form uncertainties (i) in nonlinear solid dynamics applied a to MEMS and (ii) in nonlinear computational fluid dynamics applied to a Scramjet, nonconvex optimization under uncertainties. [1] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold, Journal of Computational Physics, 321, 242-258 (2016).[2] 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, 5(1), 176-211 (2017).[3] R. Ghanem, C. Soize, Probabilistic nonconvex constrained optimization with fixed number of function evaluations, International Journal for Numerical Methods in Engineering, 113(4), 719-741 (2018).[4] C. Soize, Design optimization under uncertainties of a mesoscale implant in biological tissues using a probabilistic learning algorithm, Computational Mechanics, 62(3), 477-497 (2018).[5] C. Soize, C. Farhat, Probabilistic learning for model-form uncertainties in nonlinear computational mechanics, International Journal for Numerical Methods in Engineering, Accepted 24 October 2018.[6] C. Soize, R. Ghanem, C. Safta, X. Huan, Z.P. Vane, J. Oefelein, G. Lacaze, H.N. Najm, Enhancing model predictability for a scramjet using probabilistic learning on manifold, AIAA Journal, Accepted 13 September 2018
Nonlinear geometric modeling of uncertain structures through nonintrusive reduced-order modeling
No full textInternational audienceOver the last two decades, maximum entropy concepts have been broadly used to model uncertainties in structures directly at the level of reduced order models (ROMs) of their response, see [1] for review. Among these investigations are a few applications of the methodology to structures in the nonlinear geometric range [2-6] in which two approaches have been used to generate the deterministic ROM on which the uncertainty is built. In the first one of these [3-6], the coefficients of the deterministic ROM are determined using a dedicated finite element strategy from which the introduction of uncertainty is then carried out straightforwardly. The second approach, exemplified solely in [2], relies on a well practiced nonintrusive technique [7] to obtain the deterministic ROM from standard/commercial finite element software. This approach faces two key challenges, of decomposition and non-positive definiteness, in transforming this ROM into one that is suitable for the uncertainty analysis. The focus of the present investigation is on efficiently resolving these two challenges and applying them to a representative set of structures in the nonlinear geometric regimes.REFERENCES[1] Soize, C., (2012). Stochastic Models of Uncertainties in Computational Mechanics. American Society of Civil Engineers.[2] Mignolet, M.P., and Soize, C., (2008). Stochastic Reduced Order Models for Uncertain Geometrically Nonlinear Dynamical Systems, Computer Methods in Applied Mechanics and Engineering 197, 3951-3963.[3] Capiez-Lernout, E., Soize, C., and Mignolet, M.P., (2014). Post-buckling nonlinear static and dynamical analyses of uncertain cylindrical shells and experimental validation, Computer Methods in Applied Mechanics and Engineering 271, 210-230.[4] Capiez-Lernout, E., Soize, C., and Mignolet, M.P., (2012). Computational Stochastic Statics of an Uncertain Curved Structure with Geometrical Nonlinearity in Three-Dimensional Elasticity, Computational Mechanics 49, 87-97.[5] Capiez-Lernout, E., and Soize, C., (2015). Uncertainty Quantification for an Industrial Mistuned Bladed Disk with Geometrical Nonlinearities, Proceeding of the ASME Turbo Expo 2015, Montreal, Quebec, Canada, June 15–19. Paper No. GT2015-42471.[6] Capiez-Lernout, E., and Soize, C., (2017). An Improvement of the Uncertainty Quantification in Computational Structural Dynamics with Nonlinear Geometrical Effects, International Journal for Uncertainty Quantification 7, 83-98. [7] Mignolet, M.P., Przekop, A., Rizzi, S.A, and Spottswood, S.M., (2013). A Review of Indirect/Non-Intrusive Reduced Order Modeling of Nonlinear Geometric Structures, Journal of Sound and Vibration, 332, 2437-2460
- …
