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We propose a novel algorithm for the approximation of surface-quasi geostrophic (SQG) flows modeled by a nonlinear partial differential equation coupling transport and fractional diffusion phenomena. The time discretization consists of an…
Recently, 3D Gaussian Splatting (3DGS) has demonstrated impressive novel view synthesis results, while allowing the rendering of high-resolution images in real-time. However, leveraging 3D Gaussians for surface reconstruction poses…
This paper aims to compare between four different types of feature extraction approaches in terms of texture segmentation. The feature extraction methods that were used for segmentation are Gabor filters (GF), Gaussian Markov random fields…
PDE-constrained optimization problems have been barely solved by radial basis functions (RBFs) methods [Pearson, 2013]. It is well known that RBF methods can attain an exponential rate of convergence when $C^{\infty}$ kernels are used,…
It is well-known that the reparameterisation gradient estimator, which exhibits low variance in practice, is biased for non-differentiable models. This may compromise correctness of gradient-based optimisation methods such as stochastic…
Probabilistic point cloud registration methods are becoming more popular because of their robustness. However, unlike point-to-plane variants of iterative closest point (ICP) which incorporate local surface geometric information such as…
We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as…
Generalization in Deep Reinforcement Learning (DRL) across unseen environment variations often requires training over a diverse set of scenarios. Many existing DRL algorithms struggle with efficiency when handling numerous variations. The…
Salient object detection(SOD) aims at locating the most significant object within a given image. In recent years, great progress has been made in applying SOD on many vision tasks. The depth map could provide additional spatial prior and…
Finite-difference (FD) modeling of seismic waves in the vicinity of dipping interfaces gives rise to artifacts. Examples are phase and amplitude errors, as well as staircase diffractions. Such errors can be reduced in two general ways. In…
Computational fluid dynamics (CFD) simulations are crucial in automotive, aerospace, maritime and medical applications, but are limited by the complexity, cost and computational requirements of directly calculating the flow, often taking…
We present a new method for the solution of PDEs on manifolds $\mathbb{M} \subset \mathbb{R}^d$ of co-dimension one using stable scale-free radial basis function (RBF) interpolation. Our method involves augmenting polyharmonic spline (PHS)…
This paper introduces an innovative end-to-end model-based deep learning approach for efficient electromagnetic analysis of high-dimensional frequency selective surfaces (FSS). Unlike traditional data-driven methods that require large…
Digital twins are fundamental to the development of autonomous driving and embodied artificial intelligence. However, achieving high-granularity surface reconstruction and high-fidelity rendering remains a challenge. Gaussian splatting…
In the past decades, the finite difference methods for space fractional operators develop rapidly; to the best of our knowledge, all the existing finite difference schemes, including the first and high order ones, just work on uniform…
Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…
We describe a two-level method for computing a function whose zero-level set is the surface reconstructed from given points scattered over the surface and associated with surface normal vectors. The function is defined as a linear…
Surface reconstruction for point clouds is an important task in 3D computer vision. Most of the latest methods resolve this problem by learning signed distance functions from point clouds, which are limited to reconstructing closed…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…