Related papers: Interpolation of Discretely-Sampled Density Fields
A computationally inexpensive k.p-based interpolation scheme is developed that can extend the eigenvalues and momentum matrix elements of a sparsely sampled k-point grid into a densely sampled one. Dense sampling, often required to…
In approximation of functions based on point values, least-squares methods provide more stability than interpolation, at the expense of increasing the sampling budget. We show that near-optimal approximation error can nevertheless be…
This paper studies the role of sparse regularization in a properly chosen basis for variational data assimilation (VDA) problems. Specifically, it focuses on data assimilation of noisy and down-sampled observations while the state variable…
Infinitesimal electric and magnetic dipoles are widely used as an equivalent radiating source model. In this paper, an improved method for dipole extraction from magnitude-only electromagnetic-field data based on genetic algorithm and…
We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…
Understanding when and why interpolating methods generalize well has recently been a topic of interest in statistical learning theory. However, systematically connecting interpolating methods to achievable notions of optimality has only…
A method for data-driven interpolatory model reduction is presented in this extended abstract. This framework enables the computation of the transfer function values at given interpolation points based on time-domain input-output data only,…
In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneous case. The numerical schemes for these two settings are…
Accurate PET imaging increasingly requires methods that support unconstrained detector layouts from walk-through designs to long-axial rings where gaps and open sides lead to severely undersampled sinograms. Instead of constraining the…
We present a PDE-based approach for the multidimensional extrapolation of smooth scalar quantities across interfaces with kinks and regions of high curvature. Unlike the commonly used method of [2] in which normal derivatives are…
Despite the data labeling cost for the object detection tasks being substantially more than that of the classification tasks, semi-supervised learning methods for object detection have not been studied much. In this paper, we propose an…
An interpolation-based decoding scheme for interleaved subspace codes is presented. The scheme can be used as a (not necessarily polynomial-time) list decoder as well as a probabilistic unique decoder. Both interpretations allow to decode…
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…
Pulay's Direct Inversion in the Iterative Subspace (DIIS) method is one of the most widely used mixing schemes for accelerating the self-consistent solution of electronic structure problems. In this work, we propose a simple generalization…
Diffraction-based methods have become an invaluable tool for the detailed assessment of residual strain and stress within experimental mechanics. These methods typically measure a component of the average strain within a gauge volume. It is…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
Good generalization performance on high-dimensional data crucially hinges on a simple structure of the ground truth and a corresponding strong inductive bias of the estimator. Even though this intuition is valid for regularized models, in…
Frame interpolation is an essential video processing technique that adjusts the temporal resolution of an image sequence. While deep learning has brought great improvements to the area of video frame interpolation, techniques that make use…
This paper investigates a variational model for splines in the image metamorphosis model for the smooth interpolation of key frames in the space of images. The Riemannian manifold of images based on the metamorphosis model defines shortest…
We revisit the classical problem of 3D shape interpolation and propose a novel, physically plausible approach based on Hamiltonian dynamics. While most prior work focuses on synthetic input shapes, our formulation is designed to be…