Related papers: Spatially dependent node regularity in meshless ap…

In this work, we compare the nodal and isogeometric spatial discretization schemes for the nonlinear formulation of shear- and torsion-free rods introduced in [1]. We investigate the resulting discrete solution space, the accuracy, and the…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…

Complex phenomena can be better understood when broken down into a limited number of simpler "components". Linear statistical methods such as the principal component analysis and its variants are widely used across various fields of applied…

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a…

Accurate, global Potential Energy Surfaces (PES) expressed in sum-of-products (SOP) form are a prerequisite for efficient high-dimensional quantum dynamics simulations using the MCTDH method. This work introduces a methodology for…

In this paper, we propose a new variational framework for 3D surface denoising over triangulated meshes, which is inspired by the success of semi-sparse regularization in image processing. Differing from the uniformly sampled image data,…

Smoothed particle hydrodynamics (SPH) has been extensively used to model high and low Reynolds number flows, free surface flows and collapse of dams, study pore-scale flow and dispersion, elasticity, and thermal problems. In different…

Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…

In the present work, we investigate the computational efficiency afforded by higher-order finite-element discretization of the saddle-point formulation of orbital-free density functional theory. We first investigate the robustness of viable…

When a numerical simulation has to handle a physics problem with a wide range of time-dependent length scales, dynamically adaptive discretizations can be the method of choice. We present a major upgrade to the numerical relativity code…

Physical systems commonly exhibit spatially varying complexity, presenting a significant challenge for neural PDE solvers. While Graph Neural Networks can handle the irregular meshes required for complex geometries and boundary conditions,…

We present a semi-sparsity model for 3D triangular mesh denoising, which is motivated by the success of semi-sparsity regularization in image processing applications. We demonstrate that such a regularization model can be also applied for…

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…

In this paper we present an adaptive discretization technique for solving elliptic partial differential equations via a collocation radial basis function partition of unity method. In particular, we propose a new adaptive scheme based on…

Semantic image segmentation is one of the most important tasks in medical image analysis. Most state-of-the-art deep learning methods require a large number of accurately annotated examples for model training. However, accurate annotation…

The scattering of waves by obstacles in a 2D setting is considered, in particular the computation of the scattered field via the collocation or the least-squares methods. In the case of multiple scattering by smooth obstacles, we prove that…

We present a subspace method based on neural networks (SNN) for solving the partial differential equation with high accuracy. The basic idea of our method is to use some functions based on neural networks as base functions to span a…

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is…

In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…