17:30-17:50 Matteo Piu: Multi-Scale Modeling and Simulation of Controlled Leader-Follower Systems
Abstract: We present a multi-scale analysis of leader-follower systems under feedback control, modeled via interacting particle dynamics. Our approach follows a two-step limiting procedure: first passing to a micro-macro system coupling discrete leaders with a follower continuum, and then to a fully continuum macro-macro model. Each step is supported by quantitative convergence results based on modulated energy estimates and Wasserstein distances, providing a rigorous foundation for the reduction of complex controlled systems. Then, we provide a range of simulations that  illustrate the convergence results and highlight the effects of leader-follower coupling and the emergence of nonlinear phenomena. Some examples feature interaction potentials beyond the analytical setting, shedding light on the broader applicability of the model and its stability beyond the theoretical assumptions.

17:50-18:10 Ilaria Ciaramaglia: Nonlocal traffic flow models with time delay: well-posedness and numerical approximation
Abstract: Traffic flow is a complex phenomenon that significantly impacts our daily lives, the economy, and the environment. Understanding traffic behavior is essential for developing effective solutions to alleviate congestion and enhance road safety. We investigate traffic heterogeneity by introducing a mathematical model that describes the interactions between human drivers and autonomous vehicles (AVs). Specifically, we first propose a scalar macroscopic model, based on a variation of the classical Lighthill-Whitham-Richards framework, that incorporates key features of human driving behavior, such as nonzero reaction times and both short- and long-range vehicle interactions. This model serves as a foundation for a multi-class extension, allowing for a more detailed analysis of interactions among different classes of vehicles, each with distinct look-ahead distances and reaction times. Within this framework, we conduct a numerical investigation analyzing the stabilizing effect induced by the presence of AVs in a mixed autonomous/human-driven environment.

18:10-18.30 Giulia Tatafiore: An efficient semi-Lagrangian scheme for Fokker-Planck equations on unstructured grids
Abstract: Semi-Lagrangian schemes are characteristic-based methods for the numerical solution of hyperbolic partial differential equations (PDEs), which maintain stability under large Courant numbers. However, the need to locate the feet of the characteristics and the challenge of managing flux-deformed grid elements can significantly reduce efficiency  in the case of unstructured grids. In this work, we present a semi-Lagrangian scheme for Fokker-Planck equations, wherein these issues are addressed through the application of an efficiently initialized version of the Barycentric walk algorithm and the Sutherland-Hodgman algorithm, respectively.

17:30-17:50 Tommaso Tenna: Projective integration schemes for nonlinear degenerate parabolic systems
Abstract: In this talk, we present a general high-order fully explicit scheme based on projective integration methods to solve systems of degenerate parabolic equations in general dimensions. The method is based on a BGK approximation of the advection-diffusion equation, where projective integration method is introduced as time integrator to deal with the stiff relaxation term. This approach exploits the clear gap in the eigenvalues spectrum of the kinetic equation, taking into account a sequence of small time steps to damp out the stiff components, followed by an extrapolation step over a large time interval. The time step restriction on the projective step is similar to the CFL condition for advection-diffusion equations. The scheme is validated against some test cases.

17:50-18:10 Jacob Heieck: Exponential Stability of Finite-N Consensus-Based Optimization
Abstract: We study the finite-agent behavior of Consensus-Based Optimization (CBO), a recent metaheuristic for the global minimization of a function, that combines drift toward a consensus estimate with stochastic exploration. While previous analyses focus on asymptotic mean-field limits, we investigate the stability properties of CBO for finite population size N. Following a hierarchical approach, we first analyze a deterministic formulation of the algorithm and then extend our results to the fully stochastic setting governed by a system of stochastic differential equations. Our analysis reveals that essential stability properties, including almost sure and mean square exponential convergence, persist in both regimes and provides sharp quantitative estimates on the rates of convergence.

18:10-18:30 Raffaella Fiamma Cabini: A kinetic approach to consensus-based segmentation of biomedical images
Abstract: Image segmentation is an important task in the field of image processing and computer vision and it is widely used in several application areas, including the medical imaging field. We propose a new clustering method (Cabini, 2025) to solve biomedical image segmentation problems based on a kinetic version of the Hegselmann-Krause (HK) statistical mechanic’s model (Herty, 2020). The key idea of our approach is to associate to each particle/pixel a time-dependent state vector and a feature representing static characteristics of the system, i.e. the space position and the gray level of each pixel. Particles/pixels interact according to the generalized HK equation and, in a finite time, the system converges to a stable configuration where the initial states are grouped in a finite number of clusters. We include in the model a diffusion term which consent to quantify aleatoric uncertainties in the segmentation pipeline related to stochasticities in the data collection process.
The model is tested on two different MRI datasets: a brain tumor dataset and a thigh muscles one. The performances of the method are evaluated in terms of the Dice Similarity Coefficient (DSC) that quantifies the overlap between the reconstructed mask and the reference mask. The method reaches a DSC of 0,93 for the brain dataset and of 0,67 for the thigh muscles one. Our numerical experiments show that the introduced segmentation method achieves good performances for the tested images.

17:00-17:20  Suehaeng Sung: Uncertainty Quantification in Multi-Scale Modeling for Chemical Reactions
Abstract: A computational method for simulating complex systems that integrates data from multiple spatial and temporal dimensions is called multi-scale modeling. It bridges the gap between macroscopic (continuum or system-level) and microscopic (atoms or molecules) models by connecting complicated behaviors with large-scale occurrences. Microscopic techniques like DFT and molecular dynamics provide key reaction parameters, which inform mesoscale models like kinetic Monte Carlo for predicting reaction and diffusion behavior. These outputs can be further incorporated into continuum models such as computational fluid dynamics. By linking scales, multi-scale modeling enhances the understanding of kinetics and transport, improves prediction accuracy, and supports efficient process and reactor design. Uncertainty quantification (UQ) plays a pivotal role in multi-scale modeling, ensuring reliable predictions, as uncertainties from atomic-scale methods can propagate through mesoscale and macroscopic models. By carefully identifying, measuring, and controlling these uncertainties, UQ not only improves model robustness, but also raises confidence in simulation-driven insights and aids better decision-making in reactor design, process optimization, and risk assessment in chemical engineering applications.

17:20-17:40 Alessio Oliviero:
Abstract: We introduce a novel image processing approach based on optimal control of a multi-agent system, where each pixel is modelled as an agent whose colour evolves over time according to local interactions. When the interaction kernel decays sufficiently fast, established results in multi-agent systems theory ensure cluster formation. By controlling the support of the kernel over time, we guide the system to produce clusters corresponding to a colour quantisation of the original image. The segmentation is then naturally extracted from the level curves of the resulting colour field.
We frame this process as an optimal control problem, where the objective balances two competing goals: minimising the total variation of the final image and preserving fidelity to the original. To handle the high computational cost, we implement the system in CUDA C for efficient execution on GPUs. This framework offers a dynamics-based method for image simplification and segmentation, blending ideas from control theory, numerical analysis and image processing.
This is a joint work with Simone Cacace and Giuseppe Visconti.