Related papers: Robust Node Generation for Meshfree Discretization…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
This work delves into solving the two dimensional Poisson problem through the Finite Element Method which is relevant in various physical scenarios including heat conduction, electrostatics, gravity potential, and fluid dynamics. However,…
The popularity of local meshless methods in the field of numerical simulations has increased greatly in recent years. This is mainly due to the fact that they can operate on scattered nodes and that they allow a direct control over the…
Diffusion probabilistic models have quickly become a major approach for generative modeling of images, 3D geometry, video and other domains. However, to adapt diffusion generative modeling to these domains the denoising network needs to be…
The single sideband (SSB) framework of analytical electron ptychography can account for the presence of residual geometrical aberrations induced by the probe-forming lens. However, the accuracy of this aberration correction method is highly…
Controllable layout generation aims at synthesizing plausible arrangement of element bounding boxes with optional constraints, such as type or position of a specific element. In this work, we try to solve a broad range of layout generation…
We present SketchDNN, a generative model for synthesizing CAD sketches that jointly models both continuous parameters and discrete class labels through a unified continuous-discrete diffusion process. Our core innovation is Gaussian-Softmax…
This work introduces a reduced order modeling (ROM) framework for the solution of parameterized second-order linear elliptic partial differential equations formulated on unfitted geometries. The goal is to construct efficient…
In this paper we present a refined Radial Basis Function-generated Finite Difference (RBF-FD) solution for a non-Newtonian fluid in a closed differentially heated cavity. The non-Newtonian behaviour is modelled with the Ostwald-de Waele…
Domain Generalization techniques aim to enhance model robustness by simulating novel data distributions during training, typically through various augmentation or stylization strategies. However, these methods frequently suffer from limited…
Computations of incompressible flows with velocity boundary conditions require solution of a Poisson equation for pressure with all Neumann boundary conditions. Discretization of such a Poisson equation results in a rank-deficient matrix of…
Semi-lagrangian schemes for discretization of the dynamic programming principle are based on a time discretization projected on a state-space grid. The use of a structured grid makes this approach not feasible for high-dimensional problems…
Randomized smoothing (RS) has successfully been used to improve the robustness of predictions for deep neural networks (DNNs) by adding random noise to create multiple variations of an input, followed by deciding the consensus. To…
Neural Radiance Fields (NeRF) have achieved remarkable progress in neural rendering. Extracting geometry from NeRF typically relies on the Marching Cubes algorithm, which uses a hand-crafted threshold to define the level set. However, this…
The presented article contains a 2D mesh generation routine optimized with the Metropolis algorithm. The procedure enables to produce meshes with a prescribed size h of elements. These finite element meshes can serve as standard discrete…
Domain generalization (DG) aims to learn predictive models that can generalize to unseen domains. Most existing DG approaches focus on learning domain-invariant representations under the assumption of conditional distribution shift (i.e.,…
Poisson Surface Reconstruction is a widely-used algorithm for reconstructing a surface from an oriented point cloud. To facilitate applications where only partial surface information is available, or scanning is performed sequentially, a…
Reconstructing a surface from a point cloud is an underdetermined problem. We use a neural network to study and quantify this reconstruction uncertainty under a Poisson smoothness prior. Our algorithm addresses the main limitations of…
The method of regularized stokeslets is extensively used in biological fluid dynamics due to its conceptual simplicity and meshlessness. This simplicity carries a degree of cost in computational expense and accuracy because the number of…
In this paper, we present how high-order accurate solutions to elliptic partial differential equations can be achieved in arbitrary spatial domains using radial basis function-generated finite differences (RBF-FD) on unfitted node sets…