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Random field modeling and generation for stochastic multiscale analysis

Abstract : Stochastic multiscale approaches have received a growing attention over the past decades. Similarly to stochastic solvers (for uncertainty propagation), the choice and construction of probabilistic representations are now widely recognized as key ingredients for performing robust and predictive simulations. In this prospect, and as a complement to the commonly used functional (polynomial chaos) expansions, probabilistic models relying on information theory have been developed and promoted as a valuable way to address and solve under-determined statistical inverse problems in a high-dimensional setting [1]. In this talk, we specifically provide a self-contained theoretical and algorithmic treatment of information‐theoretic models for non‐Gaussian tensor-valued random fields exhibiting invariance properties under the action of a given subgroup of SO(3). To this aim, we first derive a unified probabilistic construction synthesizing both mathematical and multiscale constraints, along the lines proposed in [2]. We subsequently discuss generation issues through stochastic differential equations and construct a generation scheme able to perform efficiently, regardless of the stochastic dimension. Finally, the models and algorithms are exemplified through the multiscale analysis of a polymer-based nano-composite system described at the atomistic level. [1] C. Soize, A computational inverse method for identification of non‐gaussian random fields using the Bayesian approach in very high dimension, Computer Methods in Applied Mechanics and Engineering, 200, 3083–3099 (2011). [2] J. Guilleminot, C. Soize, Random fields with symmetry properties: Application to the mesoscopic modeling of elastic random media, SIAM Multiscale Modeling & Simulation, 11(3), 840-‐870 (2013).
Keywords : Random field
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Contributor : Christian Soize Connect in order to contact the contributor
Submitted on : Saturday, May 30, 2015 - 9:11:39 PM
Last modification on : Thursday, September 29, 2022 - 2:21:15 PM


  • HAL Id : hal-01158282, version 1



Johann Guilleminot, Christian Soize. Random field modeling and generation for stochastic multiscale analysis. UNCECOMP 2015, 1st ECCOMAS Thematic International Conference on Uncertainty Quantification in Computational Sciences and Engineering, May 2015, The Island of Crete, Greece. ⟨hal-01158282⟩



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