Related papers: PSI: Constructing ad-hoc Simplices to Interpolate …
The paper proposes a general quasi-interpolation scheme for high-dimensional function approximation. To facilitate error analysis, we view our quasi-interpolation as a two-step procedure. In the first step, we approximate a target function…
Hypergraphs are useful mathematical models for describing complex relationships among members of a structured graph, while hyperdigraphs serve as a generalization that can encode asymmetric relationships in the data. However, obtaining…
In order to generate novel 3D shapes with machine learning, one must allow for interpolation. The typical approach for incorporating this creative process is to interpolate in a learned latent space so as to avoid the problem of generating…
With lowrank approximation the storage requirements for dense data are reduced down to linear complexity and with the addition of hierarchy this also works for data without global lowrank properties. However, the lowrank factors itself are…
In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…
The application of suitable numerical boundary conditions for hyperbolic conservation laws on domains with complex geometry has become a problem with certain difficulty that has been tackled in different ways according to the nature of the…
In this paper we propose a fast algorithm for trivariate interpolation, which is based on the partition of unity method for constructing a global interpolant by blending local radial basis function interpolants and using locally supported…
This paper considers the problem of designing sparse linear tripole arrays. In such arrays at each antenna location there are three orthogonal dipoles, allowing full measurement of both the horizontal and vertical components of the received…
We propose a new method of constraining the redshifts of individual extragalactic sources based on celestial coordinates and their ensemble statistics. Techniques from integer linear programming are utilized to optimize simultaneously for…
A geometric numerical method for simulating suspensions of spherical and non-spherical particles with Stokes drag is proposed. The method combines divergence-free matrix-valued radial basis function interpolation of the fluid velocity field…
Flat optics foresees a new era of ultra-compact optical devices, where metasurfaces serve as the foundation. Conventional designs of metasurfaces start with a certain structure as the prototype, followed by an extensive parametric sweep to…
Projections (or dimensionality reduction) methods $P$ aim to map high-dimensional data to typically 2D scatterplots for visual exploration. Inverse projection methods $P^{-1}$ aim to map this 2D space to the data space to support tasks such…
The availability of reliable, high-resolution climate and weather data is important to inform long-term decisions on climate adaptation and mitigation and to guide rapid responses to extreme events. Forecasting models are limited by…
In this paper we present a new algorithm for multivariate interpolation of scattered data sets lying in convex domains $\Omega \subseteq \RR^N$, for any $N \geq 2$. To organize the points in a multidimensional space, we build a $kd$-tree…
We propose a non grid-based interpolation scheme based on the information from the data collected from the vicinity of the query point. As a non-grid-based interpolation, the data points can be distributed randomly in a small region, and…
This paper addresses the problem of generating dense point clouds from given sparse point clouds to model the underlying geometric structures of objects/scenes. To tackle this challenging issue, we propose a novel end-to-end learning-based…
Proximity maps and regions are defined based on the relative allocation of points from two or more classes in an area of interest and are used to construct random graphs called proximity catch digraphs (PCDs) which have applications in…
Given the widespread availability of grids of models for stellar atmospheres, it is necessary to recover intermediate atmospheric models by means of accurate techniques that go beyond simple linear interpolation and capture the intricacies…
Interpolation of sparse pixel information towards a dense target resolution finds its application across multiple disciplines in computer vision. State-of-the-art interpolation of motion fields applies model-based interpolation that makes…
The spherical nature of the wavefronts exhibited in the near-field of antenna arrays enables advanced beamforming capabilities, such as beampointing and beamnulling. In this paper, we exploit these properties to design a near-field beam…