Nicola Parolini

Emilia Capuano, Daniele Cerroni, Holger Marschall et al.

This work develops advanced numerical methods for free-surface simulations of polymer mixing processes, integrating a Volume of Fluid (VOF) interface-capturing approach with a non-conforming Immersed Boundary (IB) method to model two-phase flows of highly viscous polymer melts and air within partially filled rotating mixing devices, implemented within the Finite Volume OpenFOAM library. To overcome severe numerical instabilities arising from the strong viscosity contrast between polymer melts and air, a block-coupled scheme providing fully implicit viscous diffusion treatment is integrated into the VOF-IB framework, relaxing time-step stability constraints and substantially reducing computational cost with respect to standard segregated solvers. The resulting BC-VOF-IB solver is applied to industrially relevant geometries of single- and twin-screw extruders, yielding physically consistent predictions of velocity and pressure fields under partial filling conditions. While further developments, most notably the inclusion of thermal effects, remain necessary, the proposed framework represents a meaningful step toward bridging academic CFD research and the practical demands of industrial polymer processing.

Giovanni Ziarelli, Nicola Parolini, Marco Verani

Since infectious pathogens start spreading into a susceptible population, mathematical models can provide policy makers with reliable forecasts and scenario analyses, which can be concretely implemented or solely consulted. In these complex epidemiological scenarios, machine learning architectures can play an important role, since they directly reconstruct data-driven models circumventing the specific modelling choices and the parameter calibration, typical of classical compartmental models. In this work, we discuss the efficacy of Kernel Operator Learning (KOL) to reconstruct population dynamics during epidemic outbreaks, where the transmission rate is ruled by an input strategy. In particular, we introduce two surrogate models, named KOL-m and KOL-$\partial$, which reconstruct in two different ways the evolution of the epidemics. Moreover, we evaluate the generalization performances of the two approaches with different kernels, including the Neural Tangent Kernels, and compare them with a classical neural network model learning method. Employing synthetic but semi-realistic data, we show how the two introduced approaches are suitable for realizing fast and robust forecasts and scenario analyses, and how these approaches are competitive for determining optimal intervention strategies with respect to specific performance measures.

Giovanni Ziarelli, Stefano Pagani, Nicola Parolini et al.

In this work, we aim to formalize a novel scientific machine learning framework to reconstruct the hidden dynamics of the transmission rate, whose inaccurate extrapolation can significantly impair the quality of the epidemic forecasts, by incorporating the influence of exogenous variables (such as environmental conditions and strain-specific characteristics). We propose an hybrid model that blends a data-driven layer with a physics-based one. The data-driven layer is based on a neural ordinary differential equation that learns the dynamics of the transmission rate, conditioned on the meteorological data and wave-specific latent parameters. The physics-based layer, instead, consists of a standard SEIR compartmental model, wherein the transmission rate represents an input. The learning strategy follows an end-to-end approach: the loss function quantifies the mismatch between the actual numbers of infections and its numerical prediction obtained from the SEIR model incorporating as an input the transmission rate predicted by the neural ordinary differential equation. We validate this original approach using both a synthetic test case and a realistic test case based on meteorological data (temperature and humidity) and influenza data from Italy between 2010 and 2020. In both scenarios, we achieve low generalization error on the test set and observe strong alignment between the reconstructed model and established findings on the influence of meteorological factors on epidemic spread. Finally, we implement a data assimilation strategy to adapt the neural equation to the specific characteristics of an epidemic wave under investigation, and we conduct sensitivity tests on the network hyperparameters.