1 citations · 1 across the 10 of their papers we have counts for
11 papers
Neural-HSS: Hierarchical Semi-Separable Neural PDE Solver
Pietro Sittoni, Emanuele Zangrando, Angelo A. Casulli +2
Deep learning-based methods have shown remarkable effectiveness in solving PDEs, largely due to their ability to enable fast simulations once trained. However, despite the availabi…
Convergence of a Low-Rank Strang Splitting for Stiff Matrix Differential Equations
Carmen Scalone, Nicola Guglielmi
We propose and analyze a second-order Strang splitting method for a class of stiff matrix differential equations with Sylvester-type structure. The method splits the dynamics into…
Nonlinear Joint Spectral Radius
Piero Deidda, Nicola Guglielmi, Francesco Tudisco
We introduce a nonlinear extension of the joint spectral radius (JSR) for switched discrete-time dynamical systems governed by sub-homogeneous and order-preserving maps acting on c…
Equivalence of stationary dynamical solutions in a directed chain and a Delay Differential Equation of neuroscientific relevance
Giulio Colombini, Nicola Guglielmi, Armando Bazzani
While synchronized states, and the dynamical pathways through which they emerge, are often regarded as the paradigm to understand the dynamics of information spreading on undirecte…
Approximation properties of neural ODEs
Arturo De Marinis, Davide Murari, Elena Celledoni +3
We study the approximation properties of neural ordinary differential equations (neural ODEs) in the space of continuous functions. Since a neural ODE requires input and output dim…
Efficient Sparsification of Simplicial Complexes via Local Densities of States
Anton Savostianov, Michael T. Schaub, Nicola Guglielmi +1
Simplicial complexes (SCs) have become a popular abstraction for analyzing complex data using tools from topological data analysis or topological signal processing. However, the an…
Changing the ranking in eigenvector centrality of a weighted graph by small perturbations
Michele Benzi, Nicola Guglielmi
In this article, we consider eigenvector centrality for the nodes of a graph and study the robustness (and stability) of this popular centrality measure. For a given weighted graph…
Improving the robustness of neural ODEs with minimal weight perturbation
Arturo De Marinis, Nicola Guglielmi, Stefano Sicilia +1
We propose a method to enhance the stability of a neural ordinary differential equation (neural ODE) by reducing the maximum error growth subsequent to a perturbation of the initia…
Contractivity of neural ODEs: an eigenvalue optimization problem
Nicola Guglielmi, Arturo De Marinis, Anton Savostianov +1
We propose a novel methodology to solve a key eigenvalue optimization problem which arises in the contractivity analysis of neural ODEs. When looking at contractivity properties of…
Provable Emergence of Deep Neural Collapse and Low-Rank Bias in -Regularized Nonlinear Networks
Emanuele Zangrando, Piero Deidda, Simone Brugiapaglia +2
We present a unified theoretical framework connecting the first property of Deep Neural Collapse (DNC1) to the emergence of implicit low-rank bias in nonlinear networks trained wit…
Cholesky-like Preconditioner for Hodge Laplacians via Heavy Collapsible Subcomplex
Anton Savostianov, Francesco Tudisco, Nicola Guglielmi
Techniques based on -th order Hodge Laplacian operators are widely used to describe the topology as well as the governing dynamics of high-order systems modeled as simplic…