61 citations · 416 across the 21 of their papers we have counts for
22 papers
Asymptotic-Preserving Neural Networks for Viscoelastic Parameter Identification in Multiscale Blood Flow Modeling
Giulia Bertaglia, Raffaella Fiamma Cabini
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this…
Multi-Order Monte Carlo IMEX hierarchies for uncertainty quantification in multiscale hyperbolic systems
Giulia Bertaglia, Walter Boscheri, Lorenzo Pareschi
We introduce a novel Multi-Order Monte Carlo approach for uncertainty quantification in the context of multiscale time-dependent partial differential equations. The new framework l…
Ensemble-Based Estimation of Alzheimer's Disease Incidence from Dynamic Population Reconstructions
Giulia Bertaglia, Elisa Iacomini, Alex Viguerie
We present a two-stage methodology for reconstructing Alzheimer's disease (AD) incidence over time using ensemble Kalman inversion (EKI) applied to mortality data. In the first sta…
A PINN approach for the online identification and control of unknown PDEs
Alessandro Alla, Giulia Bertaglia, Elisa Calzola
Physics-Informed Neural Networks (PINNs) have revolutionized solving differential equations by integrating physical laws into neural networks training. This paper explores PINNs fo…
New Trends on the Systems Approach to Modeling SARS-CoV-2 Pandemics in a Globally Connected Planet
Giulia Bertaglia, Andrea Bondesan, Diletta Burini +3
This paper presents a critical analysis of the literature and perspective research ideas for modeling the epidemics caused by the SARS-CoV-2 virus. It goes beyond deterministic pop…
Modelling contagious viral dynamics: a kinetic approach based on mutual utility
Giulia Bertaglia, Lorenzo Pareschi, Giuseppe Toscani
The temporal evolution of a contagious viral disease is modelled as the dynamic progression of different classes of population with individuals interacting pairwise. This interacti…
Nonconforming Virtual Element basis functions for space-time Discontinuous Galerkin schemes on unstructured Voronoi meshes
Walter Boscheri, Giulia Bertaglia
We introduce a new class of Discontinuous Galerkin (DG) methods for solving nonlinear conservation laws on unstructured Voronoi meshes that use a nonconforming Virtual Element basi…
Gradient-based Monte Carlo methods for relaxation approximations of hyperbolic conservation laws
Giulia Bertaglia, Lorenzo Pareschi, Russel E. Caflisch
Particle methods based on evolving the spatial derivatives of the solution were originally introduced to simulate reaction-diffusion processes, inspired by vortex methods for the N…
A new family of semi-implicit Finite Volume / Virtual Element methods for incompressible flows on unstructured meshes
Walter Boscheri, Andrea Chiozzi, Michele Giuliano Carlino +1
We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. Th…
Multiscale constitutive framework of 1D blood flow modeling: Asymptotic limits and numerical methods
Giulia Bertaglia, Lorenzo Pareschi
In this paper, a multiscale constitutive framework for one-dimensional blood flow modeling is presented and discussed. By analyzing the asymptotic limits of the proposed model, it…
Asymptotic-Preserving Neural Networks for hyperbolic systems with diffusive scaling
Giulia Bertaglia
With the rapid advance of Machine Learning techniques and the deep increase of availability of scientific data, data-driven approaches have started to become progressively popular…
Asymptotic-Preserving Neural Networks for multiscale hyperbolic models of epidemic spread
Giulia Bertaglia, Chuan Lu, Lorenzo Pareschi +1
When investigating epidemic dynamics through differential models, the parameters needed to understand the phenomenon and to simulate forecast scenarios require a delicate calibrati…
Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties
Giulia Bertaglia, Liu Liu, Lorenzo Pareschi +1
Uncertainty in data is certainly one of the main problems in epidemiology, as shown by the recent COVID-19 pandemic. The need for efficient methods capable of quantifying uncertain…
Kinetic modelling of epidemic dynamics: social contacts, control with uncertain data, and multiscale spatial dynamics
Giacomo Albi, Giulia Bertaglia, Walter Boscheri +4
In this survey we report some recent results in the mathematical modeling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction be…
Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty
Giulia Bertaglia, Walter Boscheri, Giacomo Dimarco +1
In this paper we introduce a space-dependent multiscale model to describe the spatial spread of an infectious disease under uncertain data with particular interest in simulating th…
Hyperbolic compartmental models for epidemic spread on networks with uncertain data: application to the emergence of Covid-19 in Italy
Giulia Bertaglia, Lorenzo Pareschi
The importance of spatial networks in the spread of an epidemic is an essential aspect in modeling the dynamics of an infectious disease. Additionally, any realistic data-driven mo…
Modeling blood flow in networks of viscoelastic vessels with the 1-D augmented fluid-structure interaction system
Francesco Piccioli, Giulia Bertaglia, Alessandro Valiani +1
A noteworthy aspect in blood flow modeling is the definition of the mechanical interaction between the fluid flow and the biological structure that contains it, namely the vessel w…
Hyperbolic models for the spread of epidemics on networks: kinetic description and numerical methods
Giulia Bertaglia, Lorenzo Pareschi
We consider the development of hyperbolic transport models for the propagation in space of an epidemic phenomenon described by a classical compartmental dynamics. The model is base…
Uncertainty quantification of viscoelastic parameters in arterial hemodynamics with the a-FSI blood flow model
Giulia Bertaglia, Valerio Caleffi, Lorenzo Pareschi +1
This work aims at identifying and quantifying uncertainties related to elastic and viscoelastic parameters, which characterize the arterial wall behavior, in one-dimensional modeli…
Computational hemodynamics in arteries with the one-dimensional augmented fluid-structure interaction system: viscoelastic parameters estimation and comparison with in-vivo data
Giulia Bertaglia, Adrián Navas-Montilla, Alessandro Valiani +3
Mathematical models are widely recognized as a valuable tool for cardiovascular diagnosis and the study of circulatory diseases, especially to obtain data that require otherwise in…
Modeling blood flow in viscoelastic vessels: the 1D augmented fluid-structure interaction system
Giulia Bertaglia, Valerio Caleffi, Alessandro Valiani
Mathematical models and numerical simulations are widely used in the field of hemodynamics, representing a valuable resource to better understand physiological and pathological pro…
Numerical methods for hydraulic transients in visco-elastic pipes
Giulia Bertaglia, Matteo Ioriatti, Alessandro Valiani +2
A wide and critical comparison of the capability of Method of Characteristics, Explicit Path-Conservative Finite Volume Method and Semi-Implicit Staggered Finite Volume Method is p…