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Stationary points of multivariable function which represents some surface have an important role in many application such as computer vision, chemical physics, etc. Nevertheless, the dataset describing the surface for which a sampling…

Numerical Analysis · Computer Science 2018-09-07 Zuzana Majdisova , Vaclav Skala , Michal Smolik

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

Numerical Analysis · Mathematics 2013-04-30 Zhu Wang

We develop a computational approach that significantly improves the efficiency of Bayesian optimal experimental design (BOED) using local radial basis functions (RBFs). The presented RBF--BOED method uses the intrinsic ability of RBFs to…

Computational Physics · Physics 2025-05-20 Tianyi Chu , Jonathan B. Estrada , Spencer H. Bryngelson

This work aims to provide a deep-learning solution for the motion interpolation task. Previous studies solve it with geometric weight functions. Some other works propose neural networks for different problem settings with consecutive pose…

Computer Vision and Pattern Recognition · Computer Science 2023-06-13 Shuo Huang , Jia Jia , Zongxin Yang , Wei Wang , Haozhe Wu , Yi Yang , Junliang Xing

We study the trapezoidal rule for periodic functions on uniform grids and show that the quadrature error exhibits a rich deterministic structure, beyond traditional asymptotic or statistical interpretations. Focusing on the prototype…

General Mathematics · Mathematics 2025-05-06 William Cook

Planned wide-field weak lensing surveys are expected to reduce the statistical errors on the shear field to unprecedented levels. In contrast, systematic errors like those induced by the convolution with the point spread function (PSF) will…

Cosmology and Nongalactic Astrophysics · Physics 2012-10-23 M. Gentile , F. Courbin , G. Meylan

Shapley values have become a cornerstone of explainable AI, but they are computationally expensive to use, especially when features are dependent. Evaluating them requires approximating a large number of conditional expectations, either via…

Artificial Intelligence · Computer Science 2026-02-11 Lars Henry Berge Olsen , Dennis Christensen

It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…

Machine Learning · Computer Science 2026-04-17 Vladimir Fanaskov , Vladislav Trifonov , Alexander Rudikov , Ekaterina Muravleva , Ivan Oseledets

We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…

Numerical Analysis · Mathematics 2023-10-09 Simona Cucchiara , Angelo Iollo , Tommaso Taddei , Haysam Telib

Traditionally, shape transformation using implicit functions is performed in two distinct steps: 1) creating two implicit functions, and 2) interpolating between these two functions. We present a new shape transformation method that…

Graphics · Computer Science 2023-03-07 Greg Turk , James F. O'Brien

Video frame interpolation task has recently become more and more prevalent in the computer vision field. At present, a number of researches based on deep learning have achieved great success. Most of them are either based on optical flow…

Computer Vision and Pattern Recognition · Computer Science 2022-04-26 Haoyue Tian , Pan Gao , Xiaojiang Peng

This article aims to study fractal interpolation functions corresponding to a sequence of iterated function systems (IFSs). For a suitable choice of a sequence of IFS parameters, the corresponding non-stationary fractal function is a better…

Dynamical Systems · Mathematics 2023-03-22 Anarul Islam Mondal , Sangita Jha

A new method based on parameters iteration technique has been developed to determine the optimal subreflector position for shaped Cassegrain antennas to improve the electromagnetic (EM) performance distorted by gravity. Both the features of…

Instrumentation and Methods for Astrophysics · Physics 2019-04-17 Bin-bin Xiang , Cong-si Wang , Pei-yuan Lian , Na Wang , You Ban

A Radial Basis Function Generated Finite-Differences (RBF-FD) inspired technique for evaluating definite integrals over the volume of the ball in three dimensions is described. Such methods are necessary in many areas of Applied…

Numerical Analysis · Mathematics 2020-06-11 Jonah A. Reeger

Interpolatory methods offer a powerful framework for generating reduced-order models (ROMs) for non-parametric or parametric systems with time-varying inputs. Choosing the interpolation points adaptively remains an area of active interest.…

Numerical Analysis · Mathematics 2021-10-13 Sridhar Chellappa , Lihong Feng , Valentin de la Rubia , Peter Benner

We present a novel type of neural fields that uses general radial bases for signal representation. State-of-the-art neural fields typically rely on grid-based representations for storing local neural features and N-dimensional linear…

Computer Vision and Pattern Recognition · Computer Science 2023-09-28 Zhang Chen , Zhong Li , Liangchen Song , Lele Chen , Jingyi Yu , Junsong Yuan , Yi Xu

Image filters are fast, lightweight and effective, which make these conventional wisdoms preferable as basic tools in vision tasks. In practical scenarios, users have to tweak parameters multiple times to obtain satisfied results. This…

Computer Vision and Pattern Recognition · Computer Science 2022-03-02 Fu Lee Wang , Yidan Feng , Haoran Xie , Gary Cheng , Mingqiang Wei

In this paper, we investigate the application of radial basis functions (RBFs) for the approximation with collocation of the Stokes problem. The approximate solution is constructed in a multi-level fashion, each level using compactly…

Numerical Analysis · Mathematics 2014-09-29 Andrew Chernih , Quoc Thong Le Gia

Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…

Numerical Analysis · Mathematics 2018-11-07 Ben Adcock , Daan Huybrechs

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…

Numerical Analysis · Mathematics 2024-07-23 Morten E. Nielsen , Bengt Fornberg