arXiv subjects

Sofia Imperatore

Publications and source records attributed to Sofia Imperatore.

4 recordsLinked to original sources

arXiv2026

Sparse-grids-like surrogate models enhanced with gradient information

This work concerns surrogate modeling for quantities of interest (QoI) arising from parametric non-linear partial differential equations (PDEs). More specifically, we consider extending the sparse-grids surrogate modeling approach to incorporate derivatives of the QoI with respect to the PDE parameters. We discuss why this operation is not straightforward and propose a hybrid approach in which a sparse-grid scheme provides the collocation points in the parameter domain and a suitable polynomial space, but the surrogate model is built with a least-squares approach. We showcase our approach on several numerical tests, and we discuss in particular how its performance crucially depends on the relative cost and accuracy of evaluating the derivatives of the QoI compared to evaluating the QoI itself.

math.NA↗

arXiv2024

A general formulation of reweighted least squares fitting

We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when the solution is sought in any finite-dimensional vector space; secondly, to provide a general strategy to iteratively update the weights according to the approximation error and apply it to the spline fitting problem. In the experiments, we provide numerical examples for the case of polynomials and splines spaces. Subsequently, we evaluate the performance of our fitting scheme for spline curve and surface approximation, including adaptive spline constructions.

math.NA↗

arXiv2022

Artificial neural network evaluation of geometric constants for polygonal domains

We propose an approach based on Artificial Neural Networks (ANNs) to evaluate geometric constants relevant to the analysis and design of numerical schemes for partial differential equations. These constants play a central role, significantly influencing, for instance, a posteriori error estimates and the overall design of the computational strategy. Our technique leverages ANNs to learn the dependencies between these constants and a set of descriptive geometric features associated to polytopal mesh elements. The main computational costs are confined to data processing and training phases, which can be performed offline once and for all. This yields an effective tool for computing the constants, which we verify and show to be applicable across different scenarios, without substantial modifications - demonstrating its broader usability beyond the specific example considered.

math.NA↗

arXiv2020

THB-spline approximations for turbine blade design with local B-spline approximations

We consider two-stage scattered data fitting with truncated hierarchical B-splines (THB-splines) for the adaptive reconstruction of industrial models. The first stage of the scheme is devoted to the computation of local least squares variational spline approximations, exploiting a simple fairness functional to handle data distributions with a locally varying density of points. Hierarchical spline quasi-interpolation based on THB-splines is considered in the second stage of the method to construct the adaptive spline surface approximating the whole scattered data set and a suitable strategy to guide the adaptive refinement is introduced. A selection of examples on geometric models representing components of aircraft turbine blades highlights the performances of the scheme. The tests include a scattered data set with voids and the adaptive reconstruction of a cylinder-like surface.

math.NA↗