相关论文: Modeling Material Stress Using Integrated Gaussian…

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…

A simple analytical model of intergranular normal stresses is proposed for a general elastic polycrystalline material with arbitrary shaped and randomly oriented grains under uniform loading. The model provides algebraic expressions for the…

Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…

A lattice model is presented for investigating the fluctuations in static granular materials under gravitationally induced stress. The model is similar in spirit to the scalar q-model of Coppersmith et al., but ensures balance of all…

We introduce a flexible framework for modeling dependent feature allocations. Our approach addresses limitations in traditional nonparametric methods by directly modeling the logit-probability surface of the feature paintbox, enabling the…

One of the essential questions in the area of granular matter is, how to obtain macroscopic tensorial quantities like stress and strain from ``microscopic'' quantities like the contact forces in a granular assembly. Different averaging…

We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of…

Gaussian Markov random fields (GMRFs) are probabilistic graphical models widely used in spatial statistics and related fields to model dependencies over spatial structures. We establish a formal connection between GMRFs and convolutional…

Learning a Gaussian Mixture Model (GMM) is hard when the number of parameters is too large given the amount of available data. As a remedy, we propose restricting the GMM to a Gaussian Markov Random Field Mixture Model (GMRF-MM), as well as…

Simulating a depositional (or stratigraphic) sequence conditionally on borehole data is a long-standing problem in hydrogeology and in petroleum geostatistics. This paper presents a new rule-based approach for simulating depositional…

Probabilistic inference in high-dimensional state-space models is computationally challenging. For many spatiotemporal systems, however, prior knowledge about the dependency structure of state variables is available. We leverage this…

Gaussian Markov random fields (GMRFs) are frequently used as computationally efficient models in spatial statistics. Unfortunately, it has traditionally been difficult to link GMRFs with the more traditional Gaussian random field models as…

In this project, we first study the Gaussian-based hidden Markov random field (HMRF) model and its expectation-maximization (EM) algorithm. Then we generalize it to Gaussian mixture model-based hidden Markov random field. The algorithm is…

Data-based approaches are promising alternatives to the traditional analytical constitutive models for solid mechanics. Herein, we propose a Gaussian process (GP) based constitutive modeling framework, specifically focusing on planar,…

In topology optimization, the treatment of stress constraints for very large scale problems has so far not been tractable due to the failure of robust agglomeration methods, i.e. their inability to accurately handle the locality of the…

The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of…

We begin with isotropic Gaussian random fields, and show how the Bochner-Godement theorem gives a natural way to describe their covariance structure. We continue with a study of Mat\'ern processes on Euclidean space, spheres, manifolds and…

Intergranular normal stresses (INS) are critical in the initiation and evolution of grain boundary damage in polycrystalline materials. To model the effects of such microstructural damage on a macroscopic scale, knowledge of INS is usually…

Gaussian Markov random fields are used in a large number of disciplines in machine vision and spatial statistics. The models take advantage of sparsity in matrices introduced through the Markov assumptions, and all operations in inference…

In this work, we develop Gaussian process regression (GPR) models of hyperelastic material behavior. First, we consider the direct approach of modeling the components of the Cauchy stress tensor as a function of the components of the Finger…