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Diffusion probabilistic models (DPMs) are widely adopted for their outstanding generative fidelity, yet their sampling is computationally demanding. Polynomial-based multistep samplers mitigate this cost by accelerating inference; however,…

Radial basis functions are typically used when discretization sche-mes require inhomogeneous node distributions. While spawning from a desire to interpolate functions on a random set of nodes, they have found successful applications in…

We have developed a parallel algorithm for radial basis function (RBF) interpolation that exhibits O(N) complexity,requires O(N) storage, and scales excellently up to a thousand processes. The algorithm uses a GMRES iterative solver with a…

This paper presents a method to generate valid high order meshes with optimized geometrical accuracy. The high order meshing procedure starts with a linear mesh, that is subsequently curved without taking care of the validity of the high…

We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…

Using a deterministic framework allows us to estimate a function with the purpose of interpolating data in spatial statistics. Radial basis functions are commonly used for scattered data interpolation in a d-dimensional space, however,…

High-order quadrilateral meshes offer superior accuracy and computational efficiency in numerical simulations. However, existing methods struggle to simultaneously preserve boundary/interface features, ensure high quality, and achieve…

Nonlinear dimensionality reduction embeddings computed from datasets do not provide a mechanism to compute the inverse map. In this paper, we address the problem of computing a stable inverse map to such a general bi-Lipschitz map. Our…

Computational analysis with the finite element method requires geometrically accurate meshes. It is well known that high-order meshes can accurately capture curved surfaces with fewer degrees of freedom in comparison to low-order meshes.…

The computation of global radial basis function (RBF) approximations requires the solution of a linear system which, depending on the choice of RBF parameters, may be ill-conditioned. We study the stability and accuracy of approximation…

Recent progress in large-scale text-to-video (T2V) and image-to-video (I2V) diffusion models has greatly enhanced video generation, especially in terms of keyframe interpolation. However, current image-to-video diffusion models, while…

We present a Trefftz-type finite element method on meshes consisting of curvilinear polygons. Local basis functions are computed using integral equation techniques that allow for the efficient and accurate evaluation of quantities needed in…

Implicit 3D surface reconstruction of an object from its partial and noisy 3D point cloud scan is the classical geometry processing and 3D computer vision problem. In the literature, various 3D shape representations have been developed,…

In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…

We present an administration technique for the bookkeeping of adaptive mesh refinement on (hyper-)rectangular meshes. Our technique is a unified approach for h-refinement on 1-, 2- and 3D domains, which is easy to use and avoids traversing…

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…

We introduce radiance meshes, a technique for representing radiance fields with constant density tetrahedral cells produced with a Delaunay tetrahedralization. Unlike a Voronoi diagram, a Delaunay tetrahedralization yields simple triangles…

In this paper, we investigate the ruled surfaces generated by a straight line according to rotation minimizing frame (RMF). Using this frame of a straight line, we obtained the necessary and sufficient conditions when the ruled surface is…

A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernel-based interpolation (MLSKI, for short), uses both level-wise…

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…