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A Statistically Identifiable Model for Tensor-Valued Gaussian Random Variables [article]

Bruno Scalzo Dees, Anh-Huy Phan, Danilo P. Mandic
2019 arXiv   pre-print
The probabilistic framework is then generalised to describe the joint distribution of multiple tensor-valued random variables, whereby the associated mean and covariance exhibit a Khatri-Rao separable  ...  The proposed models are shown to serve as a natural basis for gridded atmospheric climate modelling.  ...  TENSOR-VALUED GAUSSIAN DISTRIBUTION The Gaussian distribution has become a ubiquitous statistical model for describing the mean and covariance structure of random variables observed across a broad variety  ... 
arXiv:1911.02915v5 fatcat:w3dor2evafgitoqlr2yvjwuagy

Non-Gaussian positive-definite matrix-valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries

J. Guilleminot, C. Soize
2011 International Journal for Numerical Methods in Engineering  
This paper is devoted to the construction of a class of prior stochastic models for non-Gaussian positive-definite matrix-valued random fields.  ...  prescribing higher statistical fluctuations in given directions.  ...  Quite recently, attention has been paid to the modeling of the randomness emphasized that a non-Gaussian tensor-valued random field cannot be constructed using nonparametric statistics, even if a large  ... 
doi:10.1002/nme.3212 fatcat:iokd243diffedmpsgbykujswby

Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data [chapter]

2012 Stochastic Models of Uncertainties in Computational Mechanics  
This paper is devoted to the identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data  ...  The experimental data sets correspond to partial experimental data made up of an observation vector which is the response of a stochastic boundary value problem depending on the tensor-valued random field  ...  The main hypotheses are thus: -a non-Gaussian tensor-valued random field must be identified, and not a realvalued random field.  ... 
doi:10.1061/9780784412237.ch08 fatcat:4q3cnxnjmjhd5o7aok4y6hr5nq

Stochastic representation for anisotropic permeability tensor random fields

Johann Guilleminot, Christian Soize, Roger G. Ghanem
2011 International journal for numerical and analytical methods in geomechanics (Print)  
Subsequently, we propose a non-parametric prior probabilistic model for non-Gaussian permeability tensor random fields, making use of the information theory and a MaxEnt procedure, and provide a physical  ...  In this paper, we introduce a novel stochastic model for the permeability tensor associated with stationary random porous media.  ...  ∈ A and I A (y) = 0 otherwise, and where N is a normalized R-valued Gaussian random variable.  ... 
doi:10.1002/nag.1081 fatcat:fnz3wdo6wnajfekwvtoh32uqam

Identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data

C. Soize
2010 Computer Methods in Applied Mechanics and Engineering  
This paper is devoted to the identification of high-dimension polynomial chaos expansions with random coefficients for non-Gaussian tensor-valued random fields using partial and limited experimental data  ...  The experimental data sets correspond to partial experimental data made up of an observation vector which is the response of a stochastic boundary value problem depending on the tensor-valued random field  ...  The main hypotheses are thus: -a non-Gaussian tensor-valued random field must be identified, and not a realvalued random field.  ... 
doi:10.1016/j.cma.2010.03.013 fatcat:taot2ylnufeixaxe35pndowtk4

A computational inverse method for identification of non-Gaussian random fields using the Bayesian approach in very high dimension

C. Soize
2011 Computer Methods in Applied Mechanics and Engineering  
This paper is devoted to the identification of Bayesian posteriors for the random coefficients of the high-dimension polynomial chaos expansions of non-Gaussian tensor-valued random fields using partial  ...  The experimental data sets correspond to an observation vector which is the response of a stochastic boundary value problem depending on the tensor-valued random field which has to be identified.  ...  Chaos Expansion (PCE) of a non-Gaussian tensor-valued random field using partial and limited experimental data.  ... 
doi:10.1016/j.cma.2011.07.005 fatcat:erg5ziupmbhirdc3cup5pin56u

Modeling of random anisotropic elastic media and impact on wave propagation

Quang-Anh Ta, Didier Clouteau, Régis Cottereau Cottereau
2010 European Journal of Computational Mechanics  
The class of stochastic non-gaussian positive-definite fields with minimal parameterization proposed by Soize (Soize, 2006) to model the elasticity tensor field of a random anisotropic material shows an  ...  Hence, the main purpose of this paper is to generalize the Soize's model in order to account independently for the anisotropy index and the fluctuation level.  ...  These moduli are then modeled as independent random variables of strictly positive real value.  ... 
doi:10.13052/ejcm.19.241-253 fatcat:hwlbgu2dtzd6lorukxyi6yrg6u

Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites

B. Staber, J. Guilleminot, C. Soize, J. Michopoulos, A. Iliopoulos
2019 Computer Methods in Applied Mechanics and Engineering  
The latter is parametrized by a set of material parameters, modeled as non-Gaussian random fields.  ...  In this paper, we investigate the construction and identification of a new random field model for representing the constitutive behavior of laminated composites.  ...  While parametric models involving a few random elastic parameters have been used for many years, information-theoretic modeling approaches in which the elasticity tensor can be treated in full as a random  ... 
doi:10.1016/j.cma.2018.12.036 fatcat:bx3lymeenzfive7tczounbki3u

Modeling of random anisotropic elastic media and impact on wave propagation

Quang-Anh Ta, Didier Clouteau, Régis Cottereau
2010 European Journal of Computational Mechanics  
The class of stochastic non-gaussian positive-definite fields with minimal parameterization proposed by Soize (Soize, 2006) to model the elasticity tensor field of a random anisotropic material shows an  ...  On montre alors que ce nouveau modèle conduit à des différences majeures dans le régime de propagation des ondes. KEYWORDS: Wave in random medium, anisotropy, random fields.  ...  These moduli are then modeled as independent random variables of strictly positive real value.  ... 
doi:10.3166/ejcm.19.241-253 fatcat:tn2mu7pr2nanjiifbqzzfk22mq

Robust Multiscale Identification of Apparent Elastic Properties at Mesoscale for Random Heterogeneous Materials with Multiscale Field Measurements

Tianyu Zhang, Florent Pled, Christophe Desceliers
2020 Materials  
Within the context of linear elasticity theory, the apparent elasticity tensor field at a given mesoscale is modeled by a prior non-Gaussian tensor-valued random field.  ...  a prior stochastic model by solving a multiscale statistical inverse problem using a stochastic computational model and some information from displacement fields at both macroscale and mesoscale.  ...  The available information for constructing the prior stochastic model of B is as follows: (i) random variables D, L and H are mutually statistically independent, (ii) random variable D takes its values  ... 
doi:10.3390/ma13122826 pmid:32586015 pmcid:PMC7345255 fatcat:njwvj5rmmzcvho3awhngdjs7nm

Mesoscale probabilistic models for the elasticity tensor of fiber reinforced composites: Experimental identification and numerical aspects

Johann Guilleminot, Christian Soize, Djimedo Kondo
2009 Mechanics of materials (Print)  
The first one was recently proposed in the literature and provides a direct stochastic representation of the mesoscopic elasticity tensor random field for anisotropic microstructures.  ...  The parameters involved in the probabilistic models are then identified and allows realizations of the random fields to be simulated by using Monte Carlo numerical simulations.  ...  Binetruy is gratefully acknowledged for having partly provided the computational and experimental ressources that were used in this study.  ... 
doi:10.1016/j.mechmat.2009.08.004 fatcat:6qqw3vsmsfbndchjuuz3c7j4qe

Stochastic prediction of high-speed train dynamics to long-term evolution of track irregularities

N. Lestoille, C. Soize, C. Funfschilling
2016 Mechanics research communications  
The long-term evolution of the vector-valued random indicator is modeled by a discrete non-Gaussian nonstationary stochastic model (ARMA type model), for which the coefficients are time-dependent.  ...  In this paper, a stochastic predictive model, based on big data made up of a lot of experimental measurements performed on the French high-speed train network, is proposed for predicting the statistical  ...  For fixed κ, G κ is a R Nη -valued Gaussian second-order centered random variable, defined on the probability space (Θ, F , P), for which the covariance matrix is the identity matrix.  ... 
doi:10.1016/j.mechrescom.2016.05.007 fatcat:em4au3rcpndejh2b2aud7artzq

A Promising Technique for Blind Identification: The Generic Statistics

Fanglin Gu, Hang Zhang, Wenwu Wang, Chunlin Xiong
2015 Circuits, systems, and signal processing  
For these reasons, a family of blind identification (BI) methods, in which the mixing matrix is obtained by decomposing the tensor constructed by the higher order derivatives of the log CAF of the observations  ...  Furthermore, we show in this paper that even if a random process is symmetrically distributed, the odd-order generic statistics are not equal to zero, while in such a case the odd-order cumulants are equal  ...  In this method, the mixing matrix is identified by decomposing a tensor formed from the generic statistics.  ... 
doi:10.1007/s00034-015-0162-x fatcat:ub2mrbxkrbcyxde3y2uafrxdcm

Stochastic Model and Generator for Random Fields with Symmetry Properties: Application to the Mesoscopic Modeling of Elastic Random Media

J. Guilleminot, C. Soize
2013 Multiscale Modeling & simulation  
This paper is concerned with the construction of a new class of generalized nonparametric probabilistic models for matrix-valued non-Gaussian random fields.  ...  The algorithm turns out to be very efficient when the stochastic dimension increases and allows for the preservation of the statistical dependence between the components of the simulated random variables  ...  The random variables [S(x)] and [A(x)] are statistically independent. 2.  ... 
doi:10.1137/120898346 fatcat:fojvoo4tpzghvaklnnxnunko5q

Causal Discovery in Knowledge Graphs by Exploiting Asymmetric Properties of Non-Gaussian Distributions [article]

Rohan Giriraj, Sinnu Susan Thomas
2021 arXiv   pre-print
The proposed approach is based around the finding of the instantaneous causal structure of a non-experimental matrix using a non-Gaussian model, i.e; finding the causal ordering of the variables in a non-Gaussian  ...  The non-experimental matrix is a low-dimensional tensor projection obtained by decomposing the adjacency tensor of a KG.  ...  To identify the scenarios where the true graph is identifiable, for which the most common example is a linear system based on non-Gaussian errors [28] .  ... 
arXiv:2106.01043v1 fatcat:mkyupdwayfgldpjmp6itj2idqe
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