Related papers: Displacement interpolation using monotone rearrang…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
Compression is a crucial solution for data reduction in modern scientific applications due to the exponential growth of data from simulations, experiments, and observations. Compression with progressive retrieval capability allows users to…
Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which…
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…
It can be shown that Stable Diffusion has a permutation-invariance property with respect to the rows of Contrastive Language-Image Pretraining (CLIP) embedding matrices. This inspired the novel observation that these embeddings can…
We consider the inverse problem of the simultaneous reconstruction of the dielectric permittivity and magnetic permeability functions of the Maxwell's system in 3D with limited boundary observations of the electric field. The theoretical…
The interpolation on Grassmann manifolds in the framework of parametric evolution partial differential equations is presented. Interpolation points on the Grassmann manifold are the subspaces spanned by the POD bases of the available…
We first consider the problem of approximating a few eigenvalues of a rational matrix-valued function closest to a prescribed target. It is assumed that the proper rational part of the rational matrix-valued function is expressed in the…
Richardson extrapolation is a classical technique from numerical analysis that can improve the approximation error of an estimation method by combining linearly several estimates obtained from different values of one of its hyperparameters,…
This work investigates the stability of (discrete) empirical interpolation for nonlinear model reduction and state field approximation from measurements. Empirical interpolation derives approximations from a few samples (measurements) via…
We present a local interpolation method in four dimensions utilising cubic splines. An extension of the three-dimensional tricubic method, the interpolated function has C$^1$ continuity and its partial derivatives are analytically…
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…
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…
The problems of computational data processing involving regression, interpolation, reconstruction and imputation for multidimensional big datasets are becoming more important these days, because of the availability of data and their widely…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
Machine learning systems, especially with overparameterized deep neural networks, can generalize to novel test instances drawn from the same distribution as the training data. However, they fare poorly when evaluated on out-of-support test…
This paper investigates the shape reconstructions of sub-wavelength objects from near-field measurements in transverse electromagnetic scattering. This geometric inverse problem is notoriously ill-posed and challenging. We develop a novel…
We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…
This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity…