Related papers: Stochastic Modelling of Elasticity Tensor Fields
Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…
We present a general, constructive procedure to find the basis for tensors of arbitrary order subject to linear constraints by transforming the problem to that of finding the nullspace of a linear operator. The proposed method utilizes…
How can one analyze detailed 3D biological objects, such as neurons and botanical trees, that exhibit complex geometrical and topological variation? In this paper, we develop a novel mathematical framework for representing, comparing, and…
As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also…
We propose a numerical strategy to generate the anisotropic meshes and select the appropriate stabilized parameters simultaneously for two dimensional convection-dominated convection-diffusion equations by stabilized continuous linear…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
Random fields are useful mathematical tools for representing natural phenomena with complex dependence structures in space and/or time. In particular, the Gaussian random field is commonly used due to its attractive properties and…
For each of the $8$ isotropy classes of elastic materials, we consider a homogeneous random field taking values in the fixed point set $\mathsf{V}$ of the corresponding class, that is isotropic with respect to the natural orthogonal…
Supervised learning by extreme learning machines resp. neural networks with random weights is studied under a non-stationary spatial-temporal sampling design which especially addresses settings where an autonomous object moving in a…
Many real-world dynamical systems can be described as State-Space Models (SSMs). In this formulation, each observation is emitted by a latent state, which follows first-order Markovian dynamics. A Probabilistic Deep SSM (ProDSSM)…
The stochastic interpolant framework offers a powerful approach for constructing generative models based on ordinary differential equations (ODEs) or stochastic differential equations (SDEs) to transform arbitrary data distributions.…
Stochastic partial differential equations (SPDEs) are ubiquitous in engineering and computational sciences. The stochasticity arises as a consequence of uncertainty in input parameters, constitutive relations, initial/boundary conditions,…
This paper introduces a new methodology to analyse bipartite and unipartite networks with nonnegative edge values. The proposed approach combines and adapts a number of ideas from the literature on latent variable network models. The…
A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding…
This work introduces and analyzes B-spline approximation spaces defined on general geometric domains obtained through a mapping from a parameter domain. These spaces are constructed as sparse-grid tensor products of univariate spaces in the…
We develop a computational framework to quantify uncertainty in shear elastography imaging of anomalies in tissues. We adopt a Bayesian inference formulation. Given the observed data, a forward model and their uncertainties, we find the…
The elastoresistivity tensor $m_{ij,kl}$ characterizes changes in a material's resistivity due to strain. As a fourth-rank tensor, elastoresistivity can be a uniquely useful probe of the symmetries and character of the electronic state of a…
Despite the ability of text-to-image models to generate high-quality, realistic, and diverse images, they face challenges in compositional generation, often struggling to accurately represent details specified in the input prompt. A…
Accurate and reliable forecasting of epidemic incidences is critical for public health preparedness, yet it remains a challenging task due to complex nonlinear temporal dependencies and heterogeneous spatial interactions. Often, point…
Liquid crystal elastomers represent a novel class of programmable shape-transforming materials whose shape change trajectory is encoded in the material's nematic director field. Using three-dimensional nonlinear finite element…