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Projective Norms are a class of tensor norms that map on the input and output spaces. These norms are useful for providing a measure of entanglement. Calculating the projective norms is an NP-hard problem, which creates challenges in…
We propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based…
Functionally Graded Material (FGM) is a type of advanced material consisting of two (or more) distinct substances with a constantly changing composition profile. FGM technologies have moved from their traditional use to advanced micro and…
This work proposes a Graph Neural Network (GNN) modeling approach to predict the resulting surface from a particle based fabrication process. The latter consists of spray-based printing of cementitious plaster on a wall and is facilitated…
Recent advances in novel view synthesis have enabled real-time rendering speeds with high reconstruction accuracy. 3D Gaussian Splatting (3D-GS), a foundational point-based parametric 3D scene representation, models scenes as large sets of…
Following the so-called Cracking Elements Method (CEM), recently presented in \cite{Yiming:14,Yiming:16}, we propose a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method…
Graph neural networks (GNNs) have shown significant accuracy improvements in a variety of graph learning domains, sparking considerable research interest. To translate these accuracy improvements into practical applications, it is essential…
We present a method for optimizing the location of the fermion ground-state nodes using a combination of diffusion Monte Carlo (DMC) and projected gradient descent (PGD). A PGD iteration shifts the parameters of an arbitrary node-fixing…
This short note introduces a novel diagnostic tool for evaluating the convection boundedness properties of numerical schemes across discontinuities. The proposed method is based on the convection boundedness criterion and the normalised…
Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures,…
We discuss Coarse Grid Projection (CGP) methodology as a guide for partial mesh refinement of incompressible flow computations for the first time. Based on it, if for a given spatial resolution the numerical simulation diverges or the…
Strain hardening is a key feature observed in many rocks deformed in the so-called ``semi-brittle'' regime, where both crystal plastic and brittle deformation mechanisms operate. Dislocation storage has long been recognised as a major…
The continuum dislocation dynamics framework for mesoscale plasticity is intended to capture the dislocation density evolution and the deformation of crystals when subjected to mechanical loading. It does so by solving a set of transport…
Partial Differential Equation (PDE)-based approaches have gained significant attention in image despeckling due to their strong capability to preserve structural details while suppressing noise. However, conventional second-order PDE models…
Crystal structure prediction (CSP) is crucial for identifying stable crystal structures in given systems and is a prerequisite for computational atomistic simulations. Recent advances in neural network potentials (NNPs) have reduced the…
The Tangential-Displacement Normal-Normal-Stress (TDNNS) method is a finite element method that was originally introduced for elastic solids and later extended to piezoelectric materials. It uses tangential components of the displacement…
Nanometer thin single-walled carbon nanotube (CNT) films collected from the aerosol chemical deposition reactors have gathered attention for their promising applications. Densification of these pristine films provides an important way to…
We propose new strategies to handle polygonal grids refinement based on Convolutional Neural Networks (CNNs). We show that CNNs can be successfully employed to identify correctly the "shape" of a polygonal element so as to design suitable…
A three-dimensional simulation model is proposed here to study the erosive wear of structure caused by solid particles, which accounts for the accumulation of surface deformation and degradation during the erosion process. Although there…
In this paper we study newly developed methods for linear elasticity on polyhedral meshes. Our emphasis is on applications of the methods to geological models. Models of subsurface, and in particular sedimentary rocks, naturally lead to…