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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…
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the…
The accelerated inverse design of complex material properties - such as identifying a material with a given stress-strain response over a nonlinear deformation path - holds great potential for addressing challenges from soft robotics to…
This manuscript explores a variational quantum formulation for nonlinear elasticity problems arising from hyperelastic material models, targeting near term noisy intermediate scale quantum (NISQ) devices. The approach leverages the…
The virtual element method (VEM) allows discretization of elasticity and plasticity problems with polygons in 2D and polyhedrals in 3D. The polygons (and polyhedrals) can have an arbitrary number of sides and can be concave or convex. These…
In this paper we present a novel method for an automated diagnosis of breast carcinoma through multilevel iterative variational mode decomposition (VMD) and textural features encompassing Zernaike moments, fractal dimension and entropy…
An introductory exposition of the virtual element method (VEM) is provided. The intent is to make this method more accessible to those unfamiliar with VEM. Familiarity with the finite element method for solving 2D linear elasticity problems…
Visual Foundation Models (VFMs) are becoming ubiquitous in computer vision, powering systems for diverse tasks such as object detection, image classification, segmentation, pose estimation, and motion tracking. VFMs are capitalizing on…
Numerical modeling of viscoelastic properties is critical to developing the structure-property relationship of polymer nanocomposites. While it is recognized that the altered polymer region near filler particles, the interphase,…
How to accurately measure the relevance and redundancy of features is an age-old challenge in the field of feature selection. However, existing filter-based feature selection methods cannot directly measure redundancy for continuous data.…
This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for…
Real-time vision-based system of fault detection (RVBS-FD) for freight trains is an essential part of ensuring railway transportation safety. Most existing vision-based methods still have high computational costs based on convolutional…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…
We propose Flexible Vertical Federated Learning (Flex-VFL), a distributed machine algorithm that trains a smooth, non-convex function in a distributed system with vertically partitioned data. We consider a system with several parties that…
A recently proposed node-based uniform strain virtual element method (NVEM) is here extended to small strain elastoplastic solids. In the proposed method, the strain is averaged at the nodes from the strain of surrounding linearly precise…
Although Convolutional Neural Networks (CNNs) have achieved promising results in image classification, they still are vulnerable to affine transformations including rotation, translation, flip and shuffle. The drawback motivates us to…
Recovering the shape and appearance of real-world objects from natural 2D images is a long-standing and challenging inverse rendering problem. In this paper, we introduce a novel hybrid differentiable rendering method to efficiently…
We propose the Vortex Particle Flow Map (VPFM) method to simulate incompressible flow with complex vortical evolution in the presence of dynamic solid boundaries. The core insight of our approach is that vorticity is an ideal quantity for…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one…