arXiv subjects

Nadaniela Egidi

Publications and source records attributed to Nadaniela Egidi.

6 recordsLinked to original sources

arXiv2026

Results, challenges and new steps on RBF approximation and computation

We present an up-to-date overview of approximation methods based on Radial Basis Function (RBF) techniques, which have recently attracted attention across various computational tools and application fields. This review study presents relevant results on RBF techniques, highlighting the associated computational challenges and stability issues that must be addressed when high-performance or parallel computation is required.

math.NA↗

arXiv2025

Inverse modeling of porous flow through deep neural networks: the case of coffee percolation

This work addresses the inverse problem of espresso coffee extraction, in which one aims to reconstruct the brewing conditions that generate a desired chemical profile in the final beverage. Starting from a high-fidelity multiphysics percolation model, describing fluid flow, solute transport, solid, liquid reactions, and heat exchange within the coffee bed, we derive a reduced forward operator mapping controllable brewing parameters to the concentrations of the main chemical species in the cup. From a mathematical standpoint, we formalize the structural requirements for the local solvability of inverse problems, providing a minimal analytical condition for the existence of a (local) inverse map: continuous differentiability of the forward operator and a locally constant, nondegenerate Jacobian rank. Under these assumptions, the Constant Rank Theorem ensures that the image of the forward operator is a smooth embedded manifold on which well-defined local right-inverses exist. Extensive experiments, including off-grid validation, show that the learned inverse map accurately reconstructs brewing temperature, grind size, and powder composition. The resulting framework combines rigorous analytical guarantees with modern data-driven methods, providing a principled and computationally efficient solution to the inverse extraction problem and enabling personalised brewing, recipe optimisation, and integration into smart coffee-machine systems.

math.NA↗

arXiv2025

The RBF Collocation Method to Design a Digital Twin for Coffee Percolation

Espresso coffee extraction is a complex physico-chemical process and can be modeled through a system of coupled partial differential equations. We present a numerical solution based on a meshless Collocation Method using Radial Basis Functions and Kansa's approach, which reveals to be accurate and robust in comparison to a reference numerical solution provided by a well-known simulation software.

math.NA↗

arXiv2024

Image Processing for Motion Magnification

Motion Magnification (MM) is a collection of relative recent techniques within the realm of Image Processing. The main motivation of introducing these techniques in to support the human visual system to capture relevant displacements of an object of interest; these motions can be in object color and in object location. In fact, the goal is to opportunely process a video sequence to obtain as output a new video in which motions are magnified and visible to the viewer. We propose a numerical technique using the Phase-Based Motion Magnification which analyses the video sequence in the Fourier Domain and rely on the Fourier Shifting Property. We describe the mathematical foundation of this method and the corresponding implementation in a numerical algorithm. We present preliminary experiments, focusing on some basic test made up using synthetic images.

cs.CV↗

arXiv2022

Computational issues by interpolating with inverse multiquadrics: a solution

We consider the interpolation problem with the inverse multiquadric radial basis function. The problem usually produces a large dense linear system that has to be solved by iterative methods. The efficiency of such methods is strictly related to the computational cost of the multiplication between the coefficient matrix and the vectors computed by the solver at each iteration. We propose an efficient technique for the calculation of the product of the coefficient matrix and a generic vector. This computation is mainly based on the well-known spectral decomposition in spherical coordinates of the Green's function of the Laplacian operator. We also show the efficiency of the proposed method through numerical simulations.

math.NA↗

arXiv2021

Inverse heat conduction to model and optimise a geothermal field

The design of heat exchanger fields is a key phase to ensure the long-term sustainability of such renewable energy systems. This task has to be accomplished by modelling the relevant processes in the complex system made up of different exchangers, where the heat transfer must be considered within exchangers and outside exchangers. We propose a mathematical model for the study of the heat conduction into the soil as consequence of the presence of exchangers. Such a problem is formulated and solved with an analytical approach. On the basis of such analytical solution, we propose an optimisation procedure to compute the best position of the exchangers by minimising the adverse effects of neighbouring devices. Some numerical experiments are used to show the effectiveness of the proposed method also by taking into account a reference approximation procedure of the problem based on a finite difference method.

math.NA↗