arXiv subjects

Salvatore Cuomo

Publications and source records attributed to Salvatore Cuomo.

14 recordsLinked to original sources

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

Towards One-shot Federated Learning: Advances, Challenges, and Future Directions

One-shot FL enables collaborative training in a single round, eliminating the need for iterative communication, making it particularly suitable for use in resource-constrained and privacy-sensitive applications. This survey offers a thorough examination of One-shot FL, highlighting its distinct operational framework compared to traditional federated approaches. One-shot FL supports resource-limited devices by enabling single-round model aggregation while maintaining data locality. The survey systematically categorizes existing methodologies, emphasizing advancements in client model initialization, aggregation techniques, and strategies for managing heterogeneous data distributions. Furthermore, we analyze the limitations of current approaches, particularly in terms of scalability and generalization in non-IID settings. By analyzing cutting-edge techniques and outlining open challenges, this survey aspires to provide a comprehensive reference for researchers and practitioners aiming to design and implement One-shot FL systems, advancing the development and adoption of One-shot FL solutions in a real-world, resource-constrained scenario.

cs.LG↗

arXiv2024

A physics-informed deep learning approach for solving strongly degenerate parabolic problems

In recent years, Scientific Machine Learning (SciML) methods for solving partial differential equations (PDEs) have gained increasing popularity. Within such a paradigm, Physics-Informed Neural Networks (PINNs) are novel deep learning frameworks for solving initial-boundary value problems involving nonlinear PDEs. Recently, PINNs have shown promising results in several application fields. Motivated by applications to gas filtration problems, here we present and evaluate a PINN-based approach to predict solutions to strongly degenerate parabolic problems with asymptotic structure of Laplacian type. To the best of our knowledge, this is one of the first papers demonstrating the efficacy of the PINN framework for solving such kind of problems. In particular, we estimate an appropriate approximation error for some test problems whose analytical solutions are fortunately known. The numerical experiments discussed include two and three-dimensional spatial domains, emphasizing the effectiveness of this approach in predicting accurate solutions.

math.NA↗

arXiv2022

Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.

cs.LG↗

arXiv2022

The effect of time discretization on the solution of parabolic PDEs with ANNs

We investigate the resolution of parabolic PDEs via Extreme Learning Machine (ELMs) Neural Networks, which have a single hidden layer and can be trained at a modest computational cost as compared with Deep Learning Neural Networks. Our approach addresses the time evolution by applying classical ODEs techniques and uses ELM-based collocation for solving the resulting stationary elliptic problems. In this framework, the $θ$-method and Backward Difference Formulae (BDF) techniques are investigated on some linear parabolic PDEs that are challeging problems for the stability and accuracy properties of the methods. The results of numerical experiments confirm that ELM-based solution techniques combined with BDF methods can provide high-accuracy solutions of parabolic PDEs.

math.NA↗

arXiv2022

A sojourn-based approach to semi-Markov Reinforcement Learning

In this paper we introduce a new approach to discrete-time semi-Markov decision processes based on the sojourn time process. Different characterizations of discrete-time semi-Markov processes are exploited and decision processes are constructed by their means. With this new approach, the agent is allowed to consider different actions depending also on the sojourn time of the process in the current state. A numerical method based on $Q$-learning algorithms for finite horizon reinforcement learning and stochastic recursive relations is investigated. Finally, we consider two toy examples: one in which the reward depends on the sojourn-time, according to the gambler's fallacy; the other in which the environment is semi-Markov even if the reward function does not depend on the sojourn time. These are used to carry on some numerical evaluations on the previously presented $Q$-learning algorithm and on a different naive method based on deep reinforcement learning.

math.PR↗

arXiv2021

Heterogeneous Data Fusion Considering Spatial Correlations using Graph Convolutional Networks and its Application in Air Quality Prediction

Heterogeneous data are commonly adopted as the inputs for some models that predict the future trends of some observations. Existing predictive models typically ignore the inconsistencies and imperfections in heterogeneous data while also failing to consider the (1) spatial correlations among monitoring points or (2) predictions for the entire study area. To address the above problems, this paper proposes a deep learning method for fusing heterogeneous data collected from multiple monitoring points using graph convolutional networks (GCNs) to predict the future trends of some observations and evaluates its effectiveness by applying it in an air quality predictions scenario. The essential idea behind the proposed method is to (1) fuse the collected heterogeneous data based on the locations of the monitoring points with regard to their spatial correlations and (2) perform prediction based on global information rather than local information. In the proposed method, first, we assemble a fusion matrix using the proposed RBF-based fusion approach; second, based on the fused data, we construct spatially and temporally correlated data as inputs for the predictive model; finally, we employ the spatiotemporal graph convolutional network (STGCN) to predict the future trends of some observations. In the application scenario of air quality prediction, it is observed that (1) the fused data derived from the RBF-based fusion approach achieve satisfactory consistency; (2) the performances of the prediction models based on fused data are better than those based on raw data; and (3) the STGCN model achieves the best performance when compared to those of all baseline models. The proposed method is applicable for similar scenarios where continuous heterogeneous data are collected from multiple monitoring points scattered across a study area.

cs.LG↗

arXiv2021

Kernel-Based Models for Influence Maximization on Graphs based on Gaussian Process Variance Minimization

The inference of novel knowledge, the discovery of hidden patterns, and the uncovering of insights from large amounts of data from a multitude of sources make Data Science (DS) to an art rather than just a mere scientific discipline. The study and design of mathematical models able to analyze information represents a central research topic in DS. In this work, we introduce and investigate a novel model for influence maximization (IM) on graphs using ideas from kernel-based approximation, Gaussian process regression, and the minimization of a corresponding variance term. Data-driven approaches can be applied to determine proper kernels for this IM model and machine learning methodologies are adopted to tune the model parameters. Compared to stochastic models in this field that rely on costly Monte-Carlo simulations, our model allows for a simple and cost-efficient update strategy to compute optimal influencing nodes on a graph. In several numerical experiments, we show the properties and benefits of this new model.

cs.LG↗

arXiv2020

Julia Language in Machine Learning: Algorithms, Applications, and Open Issues

Machine learning is driving development across many fields in science and engineering. A simple and efficient programming language could accelerate applications of machine learning in various fields. Currently, the programming languages most commonly used to develop machine learning algorithms include Python, MATLAB, and C/C ++. However, none of these languages well balance both efficiency and simplicity. The Julia language is a fast, easy-to-use, and open-source programming language that was originally designed for high-performance computing, which can well balance the efficiency and simplicity. This paper summarizes the related research work and developments in the application of the Julia language in machine learning. It first surveys the popular machine learning algorithms that are developed in the Julia language. Then, it investigates applications of the machine learning algorithms implemented with the Julia language. Finally, it discusses the open issues and the potential future directions that arise in the use of the Julia language in machine learning.

cs.LG↗

arXiv2019

Adaptive RBF Interpolation for Estimating Missing Values in Geographical Data

The quality of datasets is a critical issue in big data mining. More interesting things could be mined from datasets with higher quality. The existence of missing values in geographical data would worsen the quality of big datasets. To improve the data quality, the missing values are generally needed to be estimated using various machine learning algorithms or mathematical methods such as approximations and interpolations. In this paper, we propose an adaptive Radial Basis Function (RBF) interpolation algorithm for estimating missing values in geographical data. In the proposed method, the samples with known values are considered as the data points, while the samples with missing values are considered as the interpolated points. For each interpolated point, first, a local set of data points are adaptively determined. Then, the missing value of the interpolated point is imputed via interpolating using the RBF interpolation based on the local set of data points. Moreover, the shape factors of the RBF are also adaptively determined by considering the distribution of the local set of data points. To evaluate the performance of the proposed method, we compare our method with the commonly used k Nearest Neighbors (kNN) interpolation and Adaptive Inverse Distance Weighted (AIDW) methods, and conduct three groups of benchmark experiments. Experimental results indicate that the proposed method outperforms the kNN interpolation and AIDW in terms of accuracy, but worse than the kNN interpolation and AIDW in terms of efficiency.

math.NA↗

arXiv2018

Degree Distribution of Delaunay Triangulations

Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional Delaunay Triangulations (DTs) as a type of complex networks, and term it as DT networks. Then we statistically investigate the degree distribution of DT networks. We find that the degree distribution of DT networks well follows the Gaussian distribution in most cases, which differs from the Poisson distribution and the Power-Law distribution for the well-known Small-World networks and Scale-Free networks.

physics.soc-ph↗

arXiv2016

Computational issues and numerical experiments for Linear Multistep Method Particle Filtering

The Linear Multistep Method Particle Filter (LMM PF) is a method for predicting the evolution in time of a evolutionary system governed by a system of differential equations. If some of the parameters of the governing equations are unknowns, it is possible to organize the calculations so as to estimate them while following the evolution of the system in time. The underlying assumption in the approach that we present is that all unknowns are modelled as random variables, where the randomness is an indication of the uncertainty of their values rather than an intrinsic property of the quantities. Consequently, the states of the system and the parameters are described in probabilistic terms by their density, often in the form of representative samples. This approach is particularly attractive in the context of parameter estimation inverse problems, because the statistical formulation naturally provides a means of assessing the uncertainty in the solution via the spread of the distribution. The computational efficiency of the underlying sampling technique is crucial for the success of the method, because the accuracy of the solution depends on the ability to produce representative samples from the distribution of the unknown parameters. In this paper LMM PF is tested on a skeletal muscle metabolism problem, which was previously treated within the Ensemble Kalman filtering framework. Here numerical evidences are used to highlight the correlation between the main sources of errors and the influence of the linera multistep method adopted. Finally, we analyzed the effect of replacing LMM with Runge-Kutta class integration methods for supporting the PF technique.

math.NA↗

arXiv2013

Surface Reconstruction from Scattered Point via RBF Interpolation on GPU

In this paper we describe a parallel implicit method based on radial basis functions (RBF) for surface reconstruction. The applicability of RBF methods is hindered by its computational demand, that requires the solution of linear systems of size equal to the number of data points. Our reconstruction implementation relies on parallel scientific libraries and is supported for massively multi-core architectures, namely Graphic Processor Units (GPUs). The performance of the proposed method in terms of accuracy of the reconstruction and computing time shows that the RBF interpolant can be very effective for such problem.

cs.DC↗

arXiv2012

A PCG Implementation of an Elliptic Kernel in an Ocean Global Circulation Model Based on GPU Libraries

In this paper an inverse preconditioner for the numerical solution of an elliptic Laplace prob- lem of a global circulation ocean model is presented. The inverse preconditiong technique is adopted in order to efficiently compute the numerical solution of the elliptic kernel by using the Conjugate Gradient (CG) method. We show how the performance and the rate of conver- gence of the solver are linked to the discretized grid resolution and to the Laplace coefficients of the oceanic model. Finally, we describe an easy-to-implement version of the solver on the Graphical Processing Units (GPUs) by means of scientific computing libraries and we discuss its performance.

math.NA↗