Probabilistic learning inference constrained by an uncertain model and a target: A general method with application to elasticity homogenization without scale separation - Mechanics
Chapitre D'ouvrage Année : 2024

Probabilistic learning inference constrained by an uncertain model and a target: A general method with application to elasticity homogenization without scale separation

Résumé

We present a probabilistic learning inference that assimilates data (target set) into a parameterized large stochastic computational model resulting from discretizing a stochastic boundary value problem (BVP). A target is imposed on a vector-valued random quantity of interest (QoI), observed as the stochastic solution of the BVP. The probabilistic inference estimates the posterior probability model, which is constrained both by the second-order moment of the random residue of the BVP stochastic equations and the target set composed of statistical moments of the QoI. We assume that evaluating a single realization of the BVP is computationally expensive, so the training dataset comprises only a few points differing from big data approaches. The presented application contributes to three-dimensional stochastic homogenization of heterogeneous linear elastic media, specifically when the mesoscale and macroscale are not separated.
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Dates et versions

hal-04683074 , version 1 (01-09-2024)

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  • HAL Id : hal-04683074 , version 1

Citer

Christian Soize. Probabilistic learning inference constrained by an uncertain model and a target: A general method with application to elasticity homogenization without scale separation. F. Willot; J. Dirrenberger; S. Forest; D. Jeulin; A. Cherkaev. Continuum Models and Discrete Systems, Mathematics and Statistics 457, Springer, pp.1-14, 2024, Springer Proceedings in Mathematics & Statistics, 978-3-031-58664-4. ⟨hal-04683074⟩
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