## About

57

Publications

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1,419

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Introduction

Giacomo Albi currently works at the Department of Computer Science, University of Verona. Giacomo does research in Applied Mathematics and Analysis. Their current project is 'Kinetic and Fokker-Planck equations modeling socio-economic phenomena in multi-agent systems'.

Additional affiliations

March 2017 - present

May 2014 - March 2017

January 2011 - December 2013

Education

September 2007 - February 2010

## Publications

Publications (57)

In this paper we consider mean-field optimal control problems with selective action of the control, where the constraint is a continuity equation involving a non-local term and diffusion. First order optimality conditions are formally derived in a general framework, accounting for boundary conditions. Hence, the optimality system is used to constru...

In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse of dimensionality, the mean field formulation of the consensus control problem is considered. Although such formulation is designed to be independent of the number of agents, it is feasible to solve only f...

We consider control strategies for large--scale interacting agent systems under uncertainty. The particular focus is on the design of robust controls that allow to bound the variance of the controlled system over time. To this end we consider $\mathcal{H}_\infty$ control strategies on the agent and mean field description of the system. We show a bo...

In this paper, how to successfully and efficiently condition a target population of agents towards consensus is discussed. To overcome the curse of dimensionality, the mean field formulation of the consensus control problem is considered. Although such formulation is designed to be independent of the number of agents, it is feasible to solve only f...

Experiments in predator–prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects. However, simulating stochastic individual based models can be extremely demanding, especially when the sample...

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population. The dynamics in the control problem is characterized by the presence of an activation function which tunes the...

In this survey we report some recent results in the mathematical modelling of epidemic phenomena through the use of kinetic equations. We initially consider models of interaction between agents in which social characteristics play a key role in the spread of an epidemic, such as the age of individuals, the number of social contacts, and their econo...

In this chapter, we discuss the mathematical modeling of egressing pedestrians in an unknown environment with multiple exits. We investigate different control problems to enhance the evacuation time of a crowd of agents, by few informed individuals, named leaders. Leaders are not recognizable as such and consist of two groups: a set of unaware lead...

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 between agents in which social characteristics play a key role in the spread of an epidemic, such as the age of individuals, the number of social contacts, and their econom...

In this chapter, we discuss the mathematical modeling of egressing pedestrians in an unknown environment with multiple exits. We investigate different control problems to enhance the evacuation time of a crowd of agents, by few informed individuals, named leaders. Leaders are not recognizable as such and consist of two groups: a set of unaware lead...

We consider the construction of semi-implicit linear multistep methods that can be applied to time-dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino et al. (J. Sci. Comput. 68: 975–1001, 2016) for Runge-Kutta methods, these semi-implicit techniq...

Experiments in predator-prey systems show the emergence of long-term cycles. Deterministic model typically fails in capturing these behaviors, which emerge from the microscopic interplay of individual based dynamics and stochastic effects. However, simulating stochastic individual based models can be extremely demanding, especially when the sample...

A mean-field selective optimal control problem of multipopulation dynamics via transient leadership is considered. The agents in the system are described by their spatial position and their probability of belonging to a certain population. The dynamics in the control problem is characterized by the presence of an activation function which tunes the...

A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solvers. The training phase is enriched by the use of gradient information in the loss function, which is weighted through the use of hyper...

The adoption of containment measures to reduce the amplitude of the epidemic peak is a key aspect in tackling the rapid spread of an epidemic. Classical compartmental models must be modified and studied to correctly describe the effects of forced external actions to reduce the impact of the disease. The importance of social structure, such as the a...

A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solves. The training phase is enriched by the use gradient information in the loss function, which is weighted through the use of hyperpara...

The synthesis of control laws for interacting agent-based dynamics and their mean-field limit is studied. A linearization-based approach is used for the computation of sub-optimal feedback laws obtained from the solution of differential matrix Riccati equations. Quantification of dynamic performance of such control laws leads to theoretical estimat...

In recent decades, kinetic theory - originally developed as a field of mathematical physics - has emerged as one of the most prominent fields of modern mathematics. In recent years, there has been an explosion of applications of kinetic theory to other areas of research, such as biology and social sciences. This book collects lecture notes and rece...

In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: the first one consists in using special agents, called leaders, to steer the crowd towards the desired direction. Leaders can be either hidden in the crowd or...

After the introduction of drastic containment measures aimed at stopping the epidemic contagion from SARS-CoV2, many governments have adopted a strategy based on a periodic relaxation of such measures in the face of a severe economic crisis caused by lockdowns. Assessing the impact of such openings in relation to the risk of a resumption of the spr...

The adoption of containment measures to reduce the amplitude of the epidemic peak is a key aspect in tackling the rapid spread of an epidemic. Classical compartmental models must be modified and studied to correctly describe the effects of forced external actions to reduce the impact of the disease. The importance of social structure, such as the a...

We consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in Boscarino, Filbet and Russo (2016) for Runge-Kutta methods, these semi-implicit techniques give a great f...

In this survey we consider mathematical models and methods recently developed to control crowd dynamics, with particular emphasis on egressing pedestrians. We focus on two control strategies: The first one consists in using special agents, called leaders, to steer the crowd towards the desired direction. Leaders can be either hidden in the crowd or...

This paper presents a review and critical analysis on the modeling of the dynamics of vehicular traffic, human crowds and swarms seen as living and, hence, complex systems. It contains a survey of the kinetic models developed in the last 10 years on the aforementioned topics so that overlapping with previous reviews can be avoided. Although the mai...

We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of accuracy for Adams–Moulton and Adams–Bashforth methods, whereas BDF methods preserve high-order accuracy. Subse...

We consider the development of high order space and time numerical methods based on Implicit-Explicit (IMEX) multistep time integrators for hyperbolic systems with relaxation. More specifically, we consider hyperbolic balance laws in which the convection and the source term may have very different time and space scales. As a consequence the nature...

We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a specific strategy. By using the Boltzmann-type control approach we analyze the best-reply strategy for each leader...

We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending nonlinearly on the global state of the system at each time. We first prove the existence and uniqueness of solutions...

We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending nonlinearly on the global state of the system at each time. We first prove the existence and uniqueness of solutions...

We provide a mean-field description for a leader-follower dynamics with mass transfer among the two populations. This model allows the transition from followers to leaders and vice versa, with scalar-valued transition rates depending nonlinearly on the global state of the system at each time. We first prove the existence and uniqueness of solutions...

In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of a controller, acting in order to enhance consensus. Two types of selective controls have been presented: an homogeneous control filtered by a selective function and a distributed control active only on a se...

We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of accuracy for Adams-Moulton and Adams-Bashford methods, whereas BDF methods preserve high--order accuracy. Subse...

In this paper we are interested in the numerical solution of optimal control problems for non-linear hyperbolic conservation laws. To this aim, we consider relaxation approximations to the conservation laws coupled with the optimal control problem. Following a semi–Lagrangian interpretation of the hyperbolic relaxation system, and its adjoint count...

We study a non-local hydrodynamic system with control. First, we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then discuss the critical thresholds that lead to global regularity or finite-time blow-up of strong solutions in...

We study a multiscale approach for the control of agent-based, two-population models. The control variable acts over one population of leaders, which influence the population of followers via the coupling generated by their interaction. We cast a quadratic optimal control problem for the large-scale microscale model, which is approximated via a Bol...

We study a non-local hydrodynamic system with control. First we characterize the control dynamics as a sub-optimal approximation to the optimal control problem constrained to the evolution of the pressureless Euler alignment system. We then discuss the critical thresholds that leading to global regularity or finite-time blow-up of strong solutions...

In this paper we model the role of a government of a large population as a mean field optimal control problem. Such control problems are constrainted by a PDE of continuity-type, governing the dynamics of the probability distribution of the agent population. We show the existence of mean field optimal controls both in the stochastic and determinist...

We study the synthesis of optimal control policies for large-scale multi-agent systems. The optimal control design induces a parsimonious control intervention by means of l, sparsity-promoting control penalizations. We study instantaneous and infinite horizon sparse optimal feedback controllers. In order to circumvent the dimensionality issues asso...

We present an overview of recent analytical and numerical results for the elliptic–parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transportation networks. The model describes the pressure field using a Darcy type equation and the dynamics of the conductance network under pressure...

In this paper we consider the modeling of opinion dynamics over time dependent large scale networks. A kinetic description of the agents' distribution over the evolving network is considered which combines an opinion update based on binary interactions between agents with a dynamic creation and removal process of new connections. The number of conn...

We present an overview of recent analytical and numerical results for the elliptic–parabolic system of partial differential equations proposed by Hu and Cai, which models the formation of biological transport networks. The model describes the pressure field using a Darcy’s type equation and the dynamics of the conductance network under pressure for...

We survey some recent developments on the mathematical modeling of opinion dynamics. After an introduction on opinion modeling through interacting multi-agent systems described by partial differential equations of kinetic type, we focus our attention on two major advancements: optimal control of opinion formation and influence of additional social...

In this paper the optimal control of alignment models composed by a large number of agents is investigated in presence of a selective action of the control. As a first step toward a reduction of computational cost, we introduce a model predictive control (MPC) approximation by deriving a numerical scheme with a feedback selective constrained dynami...

In this work we are interested in the modelling and control of opinion
dynamics spreading on a time evolving network with scale-free asymptotic degree
distribution. The mathematical model is formulated as a coupling of an opinion
alignment system with a probabilistic description of the network. The optimal
control problem aims at forcing consensus...

We present a model for biological network formation originally introduced by Cai and Hu [Adaptation and optimization of biological transport networks, Phys. Rev. Lett. 111 (2013) 138701]. The modeling of fluid transportation (e.g., leaf venation and angiogenesis) and ion transportation networks (e.g., neural networks) is explained in detail and bas...

In this paper the optimal control of flocking models with random inputs is
investigated from a numerical point of view. The effect of uncertainty in the
interaction parameters is studied for a Cucker-Smale type model using a
generalized polynomial chaos (gPC) approach. Numerical evidence of threshold
effects in the alignment dynamic due to the rand...

In this paper we are concerned with multiscale modeling, control, and
simulation of self-organizing agents leaving an unknown area under limited
visibility, with special emphasis on crowds. We first introduce a new
microscopic model characterized by an exploration phase and an evacuation
phase. The main ingredients of the model are an alignment ter...

We consider the development of implicit-explicit time integration schemes for
optimal control problems governed by the Goldstein-Taylor model. In the
diffusive scaling this model is a hyperbolic approximation to the heat
equation. We investigate the relation of time integration schemes and the
formal Chapman-Enskog type limiting procedure. For the...

The study of formations and dynamics of opinions
leading to the so-called opinion consensus is one of the
most important areas in mathematical modelling of
social sciences. Following the Boltzmann-type control
approach recently introduced by the first two authors,
we consider a group of opinion leaders who modify
their strategy accordingly to an ob...

In this paper an optimal control problem for a large system of interacting
agents is considered using a kinetic perspective. As a prototype model we
analyze a microscopic model of opinion formation under constraints. For this
problem a Boltzmann-type equation based on a model predictive control
formulation is introduced and discussed. In particular...

We study the linear stability of flock and mill ring solutions of two
individual based models for biological swarming. The individuals interact via a
nonlocal interaction potential that is repulsive in the short range and
attractive in the long range. We relate the instability of the flock rings with
the instability of the ring solution of the firs...

Microscopic models of flocking and swarming takes in account large numbers of
interacting individ- uals. Numerical resolution of large flocks implies huge
computational costs. Typically for $N$ interacting individuals we have a cost
of $O(N^2)$. We tackle the problem numerically by considering approximated
binary interaction dynamics described by k...

In nature self-organized systems as flock of birds, school of fishes or herd
of sheeps have to deal with the presence of external agents such as predators
or leaders which modify their internal dynamic. Such situations take into
account a large number of individuals with their own social behavior which
interact with a few number of other individual...

## Projects

Projects (4)

- Spatial modeling of epidemic dynamics
- Modeling socially structured control actions
- Efficient numerical simulations with uncertain data

Many physical, biological, social, economic, financial systems described by PDEs involve uncertainties that must be taken into account in the mathematical models. Examples include uncertainty in the initial data and in the boundary conditions, or in the modeling parameters, like microscopic interactions, source terms, and external forces. This project focuses on the particularly challenging case represented by kinetic equations with random inputs.

Many systems of hyperbolic balance laws and kinetic equations have multiple space-time scales which made the development of efficient numerical schemes a real challenge. In this project we focus on the construction of numerical schemes for the above class of PDEs in the so-called diffusion limit.