Asymptotic preserving methods for the low Mach limit in discrete velocity models approximating kinetic equations

Giacomo Dimarco, Axel Klar, Theresa Köfler, Lorenzo Pareschi (preprint arXiv:2512.19847)

We consider a Lattice Boltzmann type discrete velocity model in the low Mach number scaling and develop a corresponding numerical scheme that remains uniformly valid across all regimes of the mean free path, from the kinetic to the hydrodynamic scale. The proposed framework ensures high order temporal accuracy through the use of Implicit Explicit Runge Kutta methods, which provide stability and efficiency in stiff regimes, while spatial resolution is enhanced by combining finite difference WENO reconstructions with high order central difference approximations.

Collective Annealing by Switching Temperatures: a Boltzmann-type description

Frédéric Blondeel, Lorenzo Pareschi, Giovanni Samaey (preprint arXiv:2512.13522)

The design of effective cooling strategies is a crucial component in simulated annealing algorithms based on the Metropolis method. Traditionally, this is achieved through inverse logarithmic decays of the temperature to ensure convergence to global minima. In this work, we propose Collective Annealing by Switching Temperatures (CAST), a novel collective simulated annealing dynamic in which agents interact to learn an adaptive cooling schedule.

High-Order Asymptotic-Preserving IMEX schemes for an ES-BGK model for Gas Mixtures

Domenico Caparello, Lorenzo Pareschi, Thomas Rey (preprint arXiv:2511.22304)

In this work we construct a high-order Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) scheme for the ES-BGK model for gas mixtures introduced in [Brull, Commun. Math. Sci., 2015]. The time discretization is based on the IMEX strategy proposed in [Filbet, Jin, J. Sci. Comput., 2011] for the single-species BGK model and is here extended to the multi-species ES-BGK setting. The resulting method is fully explicit, uniformly stable with respect to the Knudsen number and, in the fluid regime, it reduces to a consistent and high-order accurate solver for the limiting macroscopic equations of the mixture.

A DSMC-PIC coupling method for the Vlasov-Maxwell-Landau system

Andrea Medaglia, Lorenzo Pareschi, Mattia Zanella (preprint arXiv:2510.22226)

We present a numerical framework for the simulation of collisional plasma dynamics, based on a coupling between Direct Simulation Monte Carlo (DSMC) and Particle-in-Cell (PIC) methods for the Vlasov-Maxwell-Landau system. The approach extends previously developed DSMC techniques for the homogeneous Landau equation to the fully inhomogeneous, electromagnetic regime. The Landau collision operator is treated through a stochastic particle formulation inspired by the grazing-collision limit of the Boltzmann equation, which enables an efficient and physically consistent representation of Coulomb interactions without relying on the full Boltzmann structure.

Augmented data and neural networks for robust epidemic forecasting: application to COVID-19 in Italy

Giacomo Dimarco, Federica Ferrarese, Lorenzo Pareschi (preprint arXiv:2510.09192)

In this work, we propose a data augmentation strategy aimed at improving the training phase of neural networks and, consequently, the accuracy of their predictions. Our approach relies on generating synthetic data through a suitable compartmental model combined with the incorporation of uncertainty. The available data are then used to calibrate the model, which is further integrated with deep learning techniques to produce additional synthetic data for training.