102 citations · 352 across the 27 of their papers we have counts for
31 papers
Stochastic Modelling of Elasticity Tensor Fields
Sharana Kumar Shivanand, Bojana Rosić, Hermann G. Matthies
We present a novel framework for the probabilistic modelling of random fourth order material tensor fields, with a focus on tensors that are physically symmetric and positive defin…
Computing f-Divergences and Distances of High-Dimensional Probability Density Functions -- Low-Rank Tensor Approximations
Alexander Litvinenko, Youssef Marzouk, Hermann G. Matthies +2
Very often, in the course of uncertainty quantification tasks or data analysis, one has to deal with high-dimensional random variables (RVs). A high-dimensional RV can be described…
Stochastic Modelling of Symmetric Positive Definite Material Tensors
Sharana Kumar Shivanand, Bojana Rosić, Hermann G. Matthies
Spatial symmetries and invariances play an important role in the behaviour of materials and should be respected in the description and modelling of material properties. The focus h…
Machine learning-based conditional mean filter: a generalization of the ensemble Kalman filter for nonlinear data assimilation
Truong-Vinh Hoang, Sebastian Krumscheid, Hermann G. Matthies +1
This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in…
Crack propagation simulation without crack tracking algorithm: embedded discontinuity formulation with incompatible modes
A. Stanic, B. Brank, A. Ibrahimbegovic +1
We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral…
Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities
Tymofiy Gerasimov, Ulrich Römer, Jaroslav Vondřejc +2
In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit mul…
Bayesian stochastic multi-scale analysis via energy considerations
M. S. Sarfaraz, B. Rosic, H. G. Matthies +1
In this paper physical multi-scale processes governed by their own principles for evolution or equilibrium on each scale are coupled by matching the stored and dissipated energy, i…
Parametric Models Analysed with Linear Maps
Hermann G. Matthies, Roger Ohayon
Parametric entities appear in many contexts, be it in optimisation, control, modelling of random quantities, or uncertainty quantification. These are all fields where reduced order…
Parameter Identification in Viscoplasticity using Transitional Markov Chain Monte Carlo Method
Ehsan Adeli, Hermann G. Matthies
To evaluate the cyclic behavior under different loading conditions using the kinematic and isotropic hardening theory of steel, a Chaboche viscoplastic material model is employed.…
Effect of Load Path on Parameter Identification for Plasticity Models using Bayesian Methods
Ehsan Adeli, Bojana Rosić, Hermann G. Matthies +1
To evaluate the cyclic behavior under different loading conditions using the kinematic and isotropic hardening theory of steel, a Chaboche viscoplastic material model is employed.…
Post-Processing of High-Dimensional Data
Mike Espig, Wolfgang Hackbusch, Alexander Litvinenko +2
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can…
FFT-based homogenisation accelerated by low-rank tensor approximations
Jaroslav Vondřejc, Dishi Liu, Martin Ladecký +1
Fast Fourier transform (FFT) based methods have turned out to be an effective computational approach for numerical homogenisation. In particular, Fourier-Galerkin methods are compu…
Non-deterministic inference using random set models: theory, approximation, and sampling method
Truong-Vinh Hoang, Hermann G. Matthies
A random set is a generalisation of a random variable, i.e. a set-valued random variable. The random set theory allows a unification of other uncertainty descriptions such as inter…
Analysis of Probabilistic and Parametric Reduced Order Models
Hermann G. Matthies
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of wea…
Analysis of parametric models - linear methods and approximations
Hermann G. Matthies, Roger Ohayon
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- rep…
Analysis of parametric models for coupled systems
Hermann G. Matthies, Roger Ohayon
In many instances one has to deal with parametric models. Such models in vector spaces are connected to a linear map. The reproducing kernel Hilbert space and affine- / linear- rep…
Accurate computation of conditional expectation for highly non-linear problems
Jaroslav Vondřejc, Hermann G. Matthies
This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilis…
A novel reduced order model for vortex induced vibrations of long flexible cylinders
Giovanni Stabile, Hermann G. Matthies, Claudio Borri
In this manuscript the development of a reduced order model for the analysis of long flexible cylinders in an offshore environment is proposed. In particular the focus is on the mo…
Tucker Tensor analysis of Matern functions in spatial statistics
Alexander Litvinenko, David Keyes, Venera Khoromskaia +2
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required…
Bayesian Parameter Estimation via Filtering and Functional Approximations
Hermann G. Matthies, Alexander Litvinenko, Bojana V. Rosic +1
The inverse problem of determining parameters in a model by comparing some output of the model with observations is addressed. This is a description for what hat to be done to use…
Parameter Estimation via Conditional Expectation --- A Bayesian Inversion
Hermann G. Matthies, Elmar Zander, Bojana Rosic +1
When a mathematical or computational model is used to analyse some system, it is usual that some parameters resp.\ functions or fields in the model are not known, and hence uncerta…
Inverse Problems in a Bayesian Setting
Hermann G. Matthies, Elmar Zander, Bojana V. Rosić +2
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. I…
Pivoted Cholesky decomposition by Cross Approximation for efficient solution of kernel systems
Dishi Liu, Hermann G. Matthies
Large kernel systems are prone to be ill-conditioned. Pivoted Cholesky decomposition (PCD) render a stable and efficient solution to the systems without a perturbation of regulariz…
Polynomial Chaos Expansion of random coefficients and the solution of stochastic partial differential equations in the Tensor Train format
Sergey Dolgov, Boris N. Khoromskij, Alexander Litvinenko +1
We apply the Tensor Train (TT) decomposition to construct the tensor product Polynomial Chaos Expansion (PCE) of a random field, to solve the stochastic elliptic diffusion PDE with…