110 citations · 238 across the 9 of their papers we have counts for
11 papers
Probabilistic learning constrained by realizations using a weak formulation of Fourier transform of probability measures
Christian Soize
This paper deals with the taking into account a given set of realizations as constraints in the Kullback-Leibler minimum principle, which is used as a probabilistic learning algori…
Probabilistic learning inference of boundary value problem with uncertainties based on Kullback-Leibler divergence under implicit constraints
Christian Soize
In a first part, we present a mathematical analysis of a general methodology of a probabilistic learning inference that allows for estimating a posterior probability model for a st…
Stochastic elliptic operators defined by non-gaussian random fields with uncertain spectrum
Christian Soize
This paper present a construction and the analysis of a class of non-Gaussian positive-definite matrix-valued homogeneous random fields with uncertain spectral measure for stochast…
Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings
Americo Cunha, Christian Soize, Rubens Sampaio
This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory i…
Probabilistic Learning on Manifolds (PLoM) with Partition
Christian Soize, Roger Ghanem
The probabilistic learning on manifolds (PLoM) introduced in 2016 has solved difficult supervised problems for the ``small data'' limit where the number N of points in the training…
Probabilistic learning on manifolds constrained by nonlinear partial differential equations for small datasets
Christian Soize, Roger Ghanem
A novel extension of the Probabilistic Learning on Manifolds (PLoM) is presented. It makes it possible to synthesize solutions to a wide range of nonlinear stochastic boundary valu…
Probabilistic Learning on Manifolds
Christian Soize, Roger Ghanem
This paper presents mathematical results in support of the methodology of the probabilistic learning on manifolds (PLoM) recently introduced by the authors, which has been used wit…
Sampling of Bayesian posteriors with a non-Gaussian probabilistic learning on manifolds from a small dataset
Christian Soize, Roger Ghanem
This paper tackles the challenge presented by small-data to the task of Bayesian inference. A novel methodology, based on manifold learning and manifold sampling, is proposed for s…
Entropy-based closure for probabilistic learning on manifolds
C. Soizea, R. Ghanem, C. Safta +7
In a recent paper, the authors proposed a general methodology for probabilistic learning on manifolds. The method was used to generate numerical samples that are statistically cons…
Data-driven probability concentration and sampling on manifold
Christian Soize, Roger Ghanem
A new methodology is proposed for generating realizations of a random vector with values in a finite-dimensional Euclidean space that are statistically consistent with a data set o…
Random fields representations for stochastic elliptic boundary value problems and statistical inverse problems
Anthony Nouy, Christian Soize
This paper presents new results allowing an unknown non-Gaussian positive matrix-valued random field to be identified through a stochastic elliptic boundary value problem, solving…