Related papers: A meshless method to compute the proper orthogonal…
One develops a fast computational methodology for principal component analysis on manifolds. Instead of estimating intrinsic principal components on an object space with a Riemannian structure, one embeds the object space in a numerical…
In this paper we present an effective coarse space correction addressed to accelerate the solution of an algebraic linear system. The system arises from the formulation of the problem of interpolating scattered data by means of Radial Basis…
This paper describes a recent mathematical method called conflation for consolidating data from independent experiments that are designed to measure the same quantity, such as Planck's constant or the mass of the top quark. Conflation is…
Lagrangian trajectory or particle dispersion models as well as semi-Lagrangian advection schemes require meteorological data such as wind, temperature and geopotential at the exact spatio-temporal locations of the particles that move…
Learning physical dynamics from data is a fundamental challenge in machine learning and scientific modeling. Real-world observational data are inherently incomplete and irregularly sampled, posing significant challenges for existing…
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with…
Diffractive optical information processors have demonstrated significant promise in delivering high-speed, parallel, and energy efficient inference for scaling machine learning tasks. Training, however, remains a major computational…
Charts are an excellent way to convey patterns and trends in data, but they do not facilitate further modeling of the data or close inspection of individual data points. We present a fully automated system for extracting the numerical…
We suggest a method for simultaneously generating high order quadrature weights for integrals over Lipschitz domains and their boundaries that requires neither meshing nor moment computation. The weights are determined on pre-defined…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
We propose a new compressive imaging method for reconstructing 2D or 3D objects from their scattered wave-field measurements. Our method relies on a novel, nonlinear measurement model that can account for the multiple scattering phenomenon,…
The present article is concerned scattered data approximation for higher dimensional data sets which exhibit an anisotropic behavior in the different dimensions. Tailoring sparse polynomial interpolation to this specific situation, we…
A fundamental challenge in acoustic data processing is to separate a measured time series into relevant phenomenological components. A given measurement is typically assumed to be an additive mixture of myriad signals plus noise whose…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…
Matrix inversion problems are often encountered in experimental physics, and in particular in high-energy particle physics, under the name of unfolding. The true spectrum of a physical quantity is deformed by the presence of a detector,…
In this paper we present a novel particle method for the Vlasov--Poisson equation. Unlike in conventional particle methods, the particles are not interpreted as point charges, but as point values of the distribution function. In between the…
Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…
We present a new approach to factor rotation for functional data. This is achieved by rotating the functional principal components toward a predefined space of periodic functions designed to decompose the total variation into components…