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Nonlinear reduced-order models (ROMs), represented by manifold learning (ML), can effectively improve the modeling accuracy of nonlinear flow fields with discontinuities. However, the inverse mapping from low-dimensional manifold…
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…
We propose a novel meshless method to achieve super resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K Nearest Neighbor…
The interpolation-regression approximation is a powerful tool in numerical analysis for reconstructing functions defined on square or triangular domains from their evaluations at a regular set of nodes. The importance of this technique lies…
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
Video frame interpolation (VFI) is the task that synthesizes the intermediate frame given two consecutive frames. Most of the previous studies have focused on appropriate frame warping operations and refinement modules for the warped…
The paper is concerned with classic kernel interpolation methods, in addition to approximation methods that are augmented by gradient measurements. To apply kernel interpolation using radial basis functions (RBFs) in a stable way, we…
The data driven extrapolation requires the definition of a functional model depending on the available data and has the application scope of providing reliable predictions on the unknown dynamics. Since data might be scattered, we drive our…
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…
In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of…
This paper explores the generalization of the method for extracting Riemann trigonometric B-splines and Riemann kernels of trigonometric interpolation splines of arbitrary order on different grids of stitching and interpolation. It is…
Purpose: Different Magnetic resonance imaging (MRI) modalities of the same anatomical structure are required to present different pathological information from the physical level for diagnostic needs. However, it is often difficult to…
Reconstruction of density functions and their characteristic functions by radial basis functions with scattered data points is a popular topic in the theory of pricing of basket options. Such functions are usually entire or admit an…
Multiphysics simulations frequently require transferring solution fields between subproblems with non-matching spatial discretizations, typically using interpolation techniques. Standard methods are usually based on measuring the closeness…
This paper focuses on RBF-based meshless methods for approximating differential operators, one of the most popular being RBF-FD. Recently, a hybrid approach was introduced that combines RBF interpolation and traditional finite difference…
A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and…
Supervised manifold learning methods for data classification map data samples residing in a high-dimensional ambient space to a lower-dimensional domain in a structure-preserving way, while enhancing the separation between different classes…
Missing data is a ubiquitous problem. It is especially challenging in medical settings because many streams of measurements are collected at different - and often irregular - times. Accurate estimation of those missing measurements is…
The main purpose of this work is the one of providing an efficient scheme for constructing reduced interpolation models for kernel bases. In literature such problem is mainly addressed via the well-established knot insertion or knot removal…
Isosurface visualization is fundamental for exploring and analyzing 3D volumetric data. Marching cubes (MC) algorithms with linear interpolation are commonly used for isosurface extraction and visualization. Although linear interpolation is…