Alfio Borzi - Academia.edu (original) (raw)

Papers by Alfio Borzi

Research paper thumbnail of Formulation and Numerical Solution of Quantum Control Problems

Research paper thumbnail of Preconditioned Gradient Method for Data Approximation with Shallow Neural Networks

Lecture Notes in Computer Science, 2023

Research paper thumbnail of A Fokker–Planck Feedback Control-Constrained Approach for Modelling Crowd Motion

Journal of computational and theoretical transport, Jul 15, 2016

ABSTRACT A Fokker–Planck control approach to model crowd motion is investigated. This strategy is... more ABSTRACT A Fokker–Planck control approach to model crowd motion is investigated. This strategy is formulated as a bilinear optimal control-constrained problem governed by the Fokker–Planck equation modeling the evolution of the probability density function of the stochastic motion of the crowd. Theoretical results on existence and regularity of controls are provided. For computational purposes, the resulting optimality system is discretized using an alternate-direction implicit Chang–Cooper scheme that guarantees conservativeness, positivity, L2 stability, and second-order accuracy of the forward solution. A projected non-linear conjugate gradient scheme is used to solve the optimality system. Results of numerical experiments demonstrate the efficiency of the proposed control framework.

Research paper thumbnail of A Fokker-Planck Nash Game to Model Pedestrian Motion

HAL (Le Centre pour la Communication Scientifique Directe), May 1, 2017

Research paper thumbnail of 4. Single-Grid Optimization

Society for Industrial and Applied Mathematics eBooks, 2011

Research paper thumbnail of 2. Optimality Conditions

Society for Industrial and Applied Mathematics eBooks, 2011

Research paper thumbnail of Differential games

Chapman and Hall/CRC eBooks, Apr 13, 2020

Research paper thumbnail of Chapter 6: Numerical optimization methods

Research paper thumbnail of Chapter 4: Controllability of quantum systems

Research paper thumbnail of On the optimal control of random walks

IFAC-PapersOnLine, 2016

The optimal control of a class of random walks is investigated in the framework of the Chapman-Ko... more The optimal control of a class of random walks is investigated in the framework of the Chapman-Kolmogorov (CK) equation. Furthermore, the connection of this control setting with the Fokker-Planck (FP) control strategy is discussed. Results of numerical experiments validate the control framework

Research paper thumbnail of 6. PDE Optimization with Uncertainty

Society for Industrial and Applied Mathematics eBooks, 2011

Research paper thumbnail of Ecosystem models and social balance from a synchronization perspective

International Journal of Modern Physics C, Dec 8, 2021

In this paper, a connection between Heider social balance theory and synchronization patterns of ... more In this paper, a connection between Heider social balance theory and synchronization patterns of a triad of oscillators is investigated. It is shown that the Heider and Kuramoto diagrams can be identified in a way that is consistent with the interpretation of cognitive states in Heider’s theory and with the behavior of coexisting species in a network of ecosystems. While most of this work focuses on networks with predefined fixed couplings, a preliminary investigation of an evolution model for the links of the network is presented, where a universal order parameter allows to formulate a feedback of the status of the oscillators to the coupling links.

Research paper thumbnail of Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator

Applied mathematics, 2017

An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-di... more An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.

Research paper thumbnail of Robust registration of satellite images with local distortions

Research paper thumbnail of On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

Applied mathematics, 2016

A framework for the optimal sparse-control of the probability density function of a jump-diffusio... more A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-intime, tracking functionals and its L 2 -and L 1 -costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.

Research paper thumbnail of A COKOSNUT code for the control of the time-dependent Kohn–Sham model

Computer Physics Communications, May 1, 2017

Optimal control of multi-electron systems is considered in the framework of the time-dependent de... more Optimal control of multi-electron systems is considered in the framework of the time-dependent density functional theory. For this purpose, the MATLAB package COKOSNUT is presented that aims at solving optimal quantum control problems governed by the Kohn-Sham equation. This package includes a robust globalized nonlinear conjugate gradient scheme and an efficient splitting procedure for the numerical integration of the nonlinear Kohn-Sham equations in two dimensions. Results of numerical experiments demonstrate the ability of the COKOSNUT code in computing accurate optimal controls.

Research paper thumbnail of A LONE code for the sparse control of quantum systems

Computer Physics Communications, Mar 1, 2016

In many applications with quantum spin systems, control functions with a sparse and pulse-shaped ... more In many applications with quantum spin systems, control functions with a sparse and pulse-shaped structure are often required. These controls can be obtained by solving quantum optimal control problems with L1-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L1-penalized optimal control problems governed by unitary-operator quantum spin models. This package implements a new strategy that includes a globalized semi-smooth Krylov–Newton scheme and a continuation procedure. Results of numerical experiments demonstrate the ability of the LONE code in computing accurate sparse optimal control solutions.

Research paper thumbnail of Modelling with Ordinary Differential Equations

Chapman and Hall/CRC eBooks, Apr 13, 2020

Research paper thumbnail of Stability and accuracy of a pseudospectral scheme for the Wigner function equation

Numerical Methods for Partial Differential Equations, May 11, 2016

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework

Kinetic & related models, 2024

The construction of feedback-like control fields for a kinetic model in phase space is investigat... more The construction of feedback-like control fields for a kinetic model in phase space is investigated. The purpose of these controls is to drive an initial density of particles in the phase space to reach a desired cyclic trajectory and follow it in a stable way. For this purpose, an ensemble optimal control problem governed by the kinetic model is formulated in a way that is amenable to a Monte Carlo approach. The proposed formulation allows to define a oneshot solution procedure consisting in a backward solve of an augmented adjoint kinetic model. Results of numerical experiments demonstrate the effectiveness of the proposed control strategy.

Research paper thumbnail of Formulation and Numerical Solution of Quantum Control Problems

Research paper thumbnail of Preconditioned Gradient Method for Data Approximation with Shallow Neural Networks

Lecture Notes in Computer Science, 2023

Research paper thumbnail of A Fokker–Planck Feedback Control-Constrained Approach for Modelling Crowd Motion

Journal of computational and theoretical transport, Jul 15, 2016

ABSTRACT A Fokker–Planck control approach to model crowd motion is investigated. This strategy is... more ABSTRACT A Fokker–Planck control approach to model crowd motion is investigated. This strategy is formulated as a bilinear optimal control-constrained problem governed by the Fokker–Planck equation modeling the evolution of the probability density function of the stochastic motion of the crowd. Theoretical results on existence and regularity of controls are provided. For computational purposes, the resulting optimality system is discretized using an alternate-direction implicit Chang–Cooper scheme that guarantees conservativeness, positivity, L2 stability, and second-order accuracy of the forward solution. A projected non-linear conjugate gradient scheme is used to solve the optimality system. Results of numerical experiments demonstrate the efficiency of the proposed control framework.

Research paper thumbnail of A Fokker-Planck Nash Game to Model Pedestrian Motion

HAL (Le Centre pour la Communication Scientifique Directe), May 1, 2017

Research paper thumbnail of 4. Single-Grid Optimization

Society for Industrial and Applied Mathematics eBooks, 2011

Research paper thumbnail of 2. Optimality Conditions

Society for Industrial and Applied Mathematics eBooks, 2011

Research paper thumbnail of Differential games

Chapman and Hall/CRC eBooks, Apr 13, 2020

Research paper thumbnail of Chapter 6: Numerical optimization methods

Research paper thumbnail of Chapter 4: Controllability of quantum systems

Research paper thumbnail of On the optimal control of random walks

IFAC-PapersOnLine, 2016

The optimal control of a class of random walks is investigated in the framework of the Chapman-Ko... more The optimal control of a class of random walks is investigated in the framework of the Chapman-Kolmogorov (CK) equation. Furthermore, the connection of this control setting with the Fokker-Planck (FP) control strategy is discussed. Results of numerical experiments validate the control framework

Research paper thumbnail of 6. PDE Optimization with Uncertainty

Society for Industrial and Applied Mathematics eBooks, 2011

Research paper thumbnail of Ecosystem models and social balance from a synchronization perspective

International Journal of Modern Physics C, Dec 8, 2021

In this paper, a connection between Heider social balance theory and synchronization patterns of ... more In this paper, a connection between Heider social balance theory and synchronization patterns of a triad of oscillators is investigated. It is shown that the Heider and Kuramoto diagrams can be identified in a way that is consistent with the interpretation of cognitive states in Heider’s theory and with the behavior of coexisting species in a network of ecosystems. While most of this work focuses on networks with predefined fixed couplings, a preliminary investigation of an evolution model for the links of the network is presented, where a universal order parameter allows to formulate a feedback of the status of the oscillators to the coupling links.

Research paper thumbnail of Multigrid Solution of an Elliptic Fredholm Partial Integro-Differential Equation with a Hilbert-Schmidt Integral Operator

Applied mathematics, 2017

An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-di... more An efficient multigrid finite-differences scheme for solving elliptic Fredholm partial integro-differential equations (PIDE) is discussed. This scheme combines a second-order accurate finite difference discretization of the PIDE problem with a multigrid scheme that includes a fast multilevel integration of the Fredholm operator allowing the fast solution of the PIDE problem. Theoretical estimates of second-order accuracy and results of local Fourier analysis of convergence of the proposed multigrid scheme are presented. Results of numerical experiments validate these estimates and demonstrate optimal computational complexity of the proposed framework.

Research paper thumbnail of Robust registration of satellite images with local distortions

Research paper thumbnail of On Optimal Sparse-Control Problems Governed by Jump-Diffusion Processes

Applied mathematics, 2016

A framework for the optimal sparse-control of the probability density function of a jump-diffusio... more A framework for the optimal sparse-control of the probability density function of a jump-diffusion process is presented. This framework is based on the partial integro-differential Fokker-Planck (FP) equation that governs the time evolution of the probability density function of this process. In the stochastic process and, correspondingly, in the FP model the control function enters as a time-dependent coefficient. The objectives of the control are to minimize a discrete-in-time, resp. continuous-intime, tracking functionals and its L 2 -and L 1 -costs, where the latter is considered to promote control sparsity. An efficient proximal scheme for solving these optimal control problems is considered. Results of numerical experiments are presented to validate the theoretical results and the computational effectiveness of the proposed control framework.

Research paper thumbnail of A COKOSNUT code for the control of the time-dependent Kohn–Sham model

Computer Physics Communications, May 1, 2017

Optimal control of multi-electron systems is considered in the framework of the time-dependent de... more Optimal control of multi-electron systems is considered in the framework of the time-dependent density functional theory. For this purpose, the MATLAB package COKOSNUT is presented that aims at solving optimal quantum control problems governed by the Kohn-Sham equation. This package includes a robust globalized nonlinear conjugate gradient scheme and an efficient splitting procedure for the numerical integration of the nonlinear Kohn-Sham equations in two dimensions. Results of numerical experiments demonstrate the ability of the COKOSNUT code in computing accurate optimal controls.

Research paper thumbnail of A LONE code for the sparse control of quantum systems

Computer Physics Communications, Mar 1, 2016

In many applications with quantum spin systems, control functions with a sparse and pulse-shaped ... more In many applications with quantum spin systems, control functions with a sparse and pulse-shaped structure are often required. These controls can be obtained by solving quantum optimal control problems with L1-penalized cost functionals. In this paper, the MATLAB package LONE is presented aimed to solving L1-penalized optimal control problems governed by unitary-operator quantum spin models. This package implements a new strategy that includes a globalized semi-smooth Krylov–Newton scheme and a continuation procedure. Results of numerical experiments demonstrate the ability of the LONE code in computing accurate sparse optimal control solutions.

Research paper thumbnail of Modelling with Ordinary Differential Equations

Chapman and Hall/CRC eBooks, Apr 13, 2020

Research paper thumbnail of Stability and accuracy of a pseudospectral scheme for the Wigner function equation

Numerical Methods for Partial Differential Equations, May 11, 2016

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific r... more HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework

Kinetic & related models, 2024

The construction of feedback-like control fields for a kinetic model in phase space is investigat... more The construction of feedback-like control fields for a kinetic model in phase space is investigated. The purpose of these controls is to drive an initial density of particles in the phase space to reach a desired cyclic trajectory and follow it in a stable way. For this purpose, an ensemble optimal control problem governed by the kinetic model is formulated in a way that is amenable to a Monte Carlo approach. The proposed formulation allows to define a oneshot solution procedure consisting in a backward solve of an augmented adjoint kinetic model. Results of numerical experiments demonstrate the effectiveness of the proposed control strategy.