4 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…