Related papers: A variational framework for the strain-smoothed el…
In this paper, we present a novel nodal integration scheme for meshfree Galerkin methods that draws on the mathematical framework of the virtual element method. We adopt linear maximum-entropy basis functions for the discretization of field…
Sparse Autoencoders (SAEs) have emerged as a promising approach for interpreting neural network representations by learning sparse, human-interpretable features from dense activations. We investigate whether incorporating variational…
For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the classical explicit Euler scheme fails to converge strongly to the exact solution. Recently, an…
This paper studies iterative schemes for measure transfer and approximation problems, which are defined through a slicing-and-matching procedure. Similar to the sliced Wasserstein distance, these schemes benefit from the availability of…
Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown that it provides performances similar to its non-smoothed…
In this paper, we propose a general extra-gradient scheme for solving monotone variational inequalities (VI), referred to here as Approximation-based Regularized Extra-gradient method (ARE). The first step of ARE solves a VI subproblem with…
The Muon optimizer has recently demonstrated remarkable empirical success in training large language models. However, the theoretical understanding of its mechanisms remains limited. Current convergence guarantees for Muon rely heavily on…
The novel idea of weak Galerkin (WG) finite element methods is on the use of weak functions and their weak derivatives defined as distributions. Weak functions and weak derivatives can be approximated by polynomials with various degrees.…
We develop a stabilized cut finite element method for the stationary convection diffusion problem on a surface embedded in ${\mathbb{R}}^d$. The cut finite element method is based on using an embedding of the surface into a three…
In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematic hardening is analyzed. Thereby, the non-differentiability of the involved plasticity functional is resolved by a Lagrange multiplier leading…
In this paper we deal with the important problem of estimating the local strain tensor from a sequence of micro-structural images realized during deformation tests of engineering materials. Since the strain tensor is defined via the…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of…
Numerical simulations of waves in highly heterogeneous media have important applications, but direct computations are prohibitively expensive. In this paper, we develop a new generalized multiscale finite element method with the aim of…
In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure formulation. Convergence rates with one order higher than the…
This paper presents a novel mass-conservative mixed multiscale method for solving flow equations in heterogeneous porous media. The media properties (the permeability) contain multiple scales and high contrast. The proposed method solves…
This paper introduces the Strain Elevation Tension Spring embedding (SETSe) algorithm, a graph embedding method that uses a physics model to create node and edge embeddings in undirected attribute networks. Using a low-dimensional…
A new semi-discrete finite element scheme for the evolution of three parametrized curves by curvature flow that are connected by a triple junction is presented and analyzed. In this triple junction, conditions are imposed on the angles at…
This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…