Related papers: Mechanical State Estimation with a Polynomial-Chao…
Computational modelling offers a cost-effective and time-efficient alternative to experimental studies in biomedical engineering. In cardiac electro-mechanics, finite element method (FEM)-based simulations provide valuable insights into…
We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…
We introduce a new concept of sparsity for the stochastic elliptic operator $-{\rm div}\left(a(x,\omega)\nabla(\cdot)\right)$, which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially…
The phase-field approach to brittle fracture provides a continuum framework for modeling crack initiation and propagation without explicit representation of discrete crack surfaces, provided the spatial discretization is fine enough to…
We consider the problem of state estimation from limited discrete and noisy measurements. In particular, we focus on modal state estimation, which approximates the unknown state of the system within a prescribed basis. We estimate the…
The fracture simulation of random particle reinforced composite structures remains a challenge. Current techniques either assumed a homogeneous model, ignoring the microstructure characteristics of composite structures, or considered a…
A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the…
This paper considers the problem of computing Bayesian estimates of both states and model parameters for nonlinear state-space models. Generally, this problem does not have a tractable solution and approximations must be utilised. In this…
This paper presents a surrogate modelling technique based on domain partitioning for Bayesian parameter inference of highly nonlinear engineering models. In order to alleviate the computational burden typically involved in Bayesian…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…
Based on the physics of stochastic processes we present a new approach for structural health monitoring. We show that the new method allows for an in-situ analysis of the elastic features of a mechanical structure even for realistic…
Building surrogate models with uncertainty quantification capabilities is essential for many engineering applications where randomness, such as variability in material properties, is unavoidable. Polynomial Chaos Expansion (PCE) is widely…
In this paper, we propose an implicit staggered algorithm for crystal plasticity finite element method (CPFEM) which makes use of dynamic relaxation at the constitutive integration level. An uncoupled version of the constitutive system…
Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by…
Stochastic differential equation mixed-effects models (SDEMEMs) are flexible hierarchical models that are able to account for random variability inherent in the underlying time-dynamics, as well as the variability between experimental units…
We provide a concise review of the exponentially convergent multiscale finite element method (ExpMsFEM) for efficient model reduction of PDEs in heterogeneous media without scale separation and in high-frequency wave propagation. ExpMsFEM…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
A central challenge in physics is to describe non-equilibrium systems driven by randomness, such as a randomly growing interface, or fluids subject to random fluctuations that account e.g. for local stresses and heat fluxes not related to…
This paper is concerned with fully discrete mixed finite element approximations of the time-dependent stochastic Stokes equations with multiplicative noise. A prototypical method, which comprises of the Euler-Maruyama scheme for time…