Related papers: Adaptive Partition of Unity Interpolation Method w…
Partition of unity methods (PUMs) on graphs are simple and highly adaptive auxiliary tools for graph signal processing. Based on a greedy-type metric clustering and augmentation scheme, we show how a partition of unity can be generated in…
We generalize the interpolative separable density fitting (ISDF) method, used for compressing the four-index electron repulsion integral (ERI) tensor, to incorporate adaptive real space grids for potentially highly localized single-particle…
Volume conservation and shape preservation are two well-known issues related to the advection and remeshing in front tracking. To address these issues, this paper proposes a divergence-preserving velocity interpolation method and a…
We present a new technique for the interpolation of discretely-sampled non-negat ive scalar fields across regions of missing data. Any set of basis functions can be used, though the method is fastest when they are close to orthogonal. We…
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Compensated convexity methods for approximations and…
The interaction between two particles with shape or interaction anisotropy can be modeled using a pairwise potential energy function that depends on their relative position and orientation; however, this function is often challenging to…
Vision Transformers (ViTs) partition input images into uniformly sized patches regardless of their content, resulting in long input sequence lengths for high-resolution images. We present Adaptive Patch Transformers (APT), which addresses…
A piecewise Pad\'e-Chebyshev type (PiPCT) approximation method is proposed to minimize the Gibbs phenomenon in approximating piecewise smooth functions. A theorem on $L^1$-error estimate is proved for sufficiently smooth functions using a…
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase space due to their better scalability than continuum approaches with respect to dimension. Complex processes…
Image inpainting methods have shown significant improvements by using deep neural networks recently. However, many of these techniques often create distorted structures or blurry textures inconsistent with surrounding areas. The problem is…
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…
While there exists a rich array of matrix column subset selection problem (CSSP) algorithms for use with interpolative and CUR-type decompositions, their use can often become prohibitive as the size of the input matrix increases. In an…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
In computational practice, we often encounter situations where only measurements at equally spaced points are available. Using standard polynomial interpolation in such cases can lead to highly inaccurate results due to numerical…
There are numerous contexts where one wishes to describe the state of a randomly evolving system. Effective solutions combine models that quantify the underlying uncertainty with available observational data to form relatively optimal…
Image anomaly detection consists in detecting images or image portions that are visually different from the majority of the samples in a dataset. The task is of practical importance for various real-life applications like biomedical image…
Adaptive moving spatial meshes are useful for solving physical models given by time-dependent partial differentialequations. However, special consideration must be given when combining adaptive meshing procedures with ensemble-based data…
We extend the univariate Newton interpolation algorithm to arbitrary spatial dimensions and for any choice of downward-closed polynomial space, while preserving its quadratic runtime and linear storage cost. The generalisation supports any…
Mixup is a powerful data augmentation method that interpolates between two or more examples in the input or feature space and between the corresponding target labels. Many recent mixup methods focus on cutting and pasting two or more…
We introduce an $r-$adaptive algorithm to solve Partial Differential Equations using a Deep Neural Network. The proposed method restricts to tensor product meshes and optimizes the boundary node locations in one dimension, from which we…