107 citations · 475 across the 51 of their papers we have counts for
60 papers
Control Strategies for Multi-Species Wasserstein Gradient Flows
Dante Kalise, Lucas M. Moschen, Grigorios A. Pavliotis
We stabilize stationary states of coupled multi-species McKean--Vlasov equations by feedback control, extending a spectral approach based on the Wasserstein Hessian and a Riccati e…
Nonlocal Mean Field Schrödinger Bridge with Learned Interactions
Daisuke Inoue, Dante Kalise, Mathieu Laurière
The Schrödinger Bridge Problem connects an initial distribution to a terminal one along a minimum-energy stochastic process. Its mean-field extension, the Mean-Field Schrödinger Br…
Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs
Matías Gómez-Aedo, Behzad Azmi, Yuyang Huang +2
A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Princip…
A Proximal Primal-Dual Approach to Generalized JKO Schemes for Doubly Nonlinear Parabolic Equations
Luis M. Briceño-Arias, José A. Carrillo, Dante Kalise +2
Variational methods based on optimization strategies are proposed to numerically solve a large family of nonlinear partial differential equations. They are all particular instances…
Feedback Control and Local Convexification of Wasserstein Gradient Flows
Dante Kalise, Lucas M. Moschen, Grigorios A. Pavliotis
Building on the feedback stabilization framework that we developed for McKean-Vlasov PDEs, we treat a class of entropy-regularized free energies on the flat…
Sparse stabilization of mean-field agent dynamics through a three-operator splitting method
Giacomo Albi, Dante Kalise, Chiara Segala +1
We study the sparse stabilization of nonlinear multi-agent systems within a mean-field optimal control framework. The goal is to drive large populations of interacting agents towar…
Non-Convex Global Optimization as an Optimal Stabilization Problem: Dynamical Properties
Yuyang Huang, Dante Kalise, Hicham Kouhkouh
We study global optimization of non-convex functions through optimal control theory. Our main result establishes that (quasi-)optimal trajectories of a discounted control problem c…
A PDE-constrained Optimization Approach to Optimal Trajectory Planning under Uncertainty via Reflected Schrödinger Bridges
Dante Kalise, Wenxin Liu
A computational PDE-constrained optimization approach is proposed for optimal trajectory planning under uncertainty by means of an associated Schroedinger Bridge Problem (SBP). The…
Non-Convex Global Optimization as an Optimal Stabilization Problem: Convergence Rates
Yuyang Huang, Dante Kalise, Hicham Kouhkouh
We develop a rigorous framework for global non-convex optimization by reformulating the minimization problem as a discounted infinite-horizon optimal control problem. For non-conve…
An Inexact Tensor-Train Primal-Dual Interior-Point Method for Semidefinite Programs
Frederik Kelbel, Sergey Dolgov, Dante Kalise +1
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite program…
Hierarchical clustering and dimensional reduction for optimal control of large-scale agent-based models
Angela Monti, Fasma Diele, Dante Kalise
Agent-based models (ABMs) provide a powerful framework to describe complex systems composed of interacting entities, capable of producing emergent collective behaviours such as con…
Linearization-Based Feedback Stabilization of McKean-Vlasov PDEs
Dante Kalise, Lucas M. Moschen, Grigorios A. Pavliotis
We develop a feedback control framework for stabilizing the McKean-Vlasov PDE on the torus. Our goal is to steer the dynamics toward a prescribed stationary distribution or acceler…
Parallel-in-Time Preconditioning for Time-Dependent Variational Mean Field Games
Heidi Wolles Ljósheim, Dante Kalise, John W. Pearson +1
We study the numerical approximation of a time-dependent variational mean field game system with local couplings and either periodic or Neumann boundary conditions. Following a var…
Optimal Control of Thin-Film Flow on a Flexible Topography
S. Alrashidy, A. Kalogirou, D. Kalise +1
This work presents a mathematical model for the optimal control of thin-film flows over a flexible substrate influenced by an external force. The objective is to find the optimal d…
Time-optimal neural feedback control of nilpotent systems as a binary classification problem
Sara Bicego, Samuel Gue, Dante Kalise +1
A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, wh…
A Spectral Approach to Optimal Control of the Fokker-Planck Equation
Dante Kalise, Lucas M. Moschen, Grigorios A. Pavliotis +1
In this paper, we present a spectral optimal control framework for Fokker-Planck equations based on the standard ground state transformation that maps the Fokker-Planck operator to…
Separable Approximations of Optimal Value Functions and Their Representation by Neural Networks
Mario Sperl, Luca Saluzzi, Dante Kalise +1
The use of separable approximations is proposed to mitigate the curse of dimensionality related to the approximation of high-dimensional value functions in optimal control. The sep…
A polynomial approximation scheme for nonlinear model reduction by moment matching
Carlos Doebeli, Alessandro Astolfi, Dante Kalise +3
We propose a procedure for the numerical approximation of invariance equations arising in the moment matching technique associated with reduced-order modeling of high-dimensional d…
A total variation flow scheme for ergodic mean field games
Dante Kalise, Alessio Oliviero, Domènec Ruiz-Balet
Motivated by recent developments in mean field games in ecology, in this paper we introduce a connection between the best response dynamics in evolutionary game theory, the minimiz…
Fast and robust consensus-based optimization via optimal feedback control
Yuyang Huang, Michael Herty, Dante Kalise +1
We propose a variant of consensus-based optimization (CBO) algorithms, controlled-CBO, which introduces a feedback control term to improve convergence towards global minimizers of…
A multiscale Consensus-Based algorithm for multi-level optimization
Michael Herty, Yuyang Huang, Dante Kalise +1
A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the pr…
Computation and Control of Unstable Steady States for Mean Field Multiagent Systems
Sara Bicego, Dante Kalise, Grigorios A. Pavliotis
We study interacting particle systems driven by noise, modeling phenomena such as opinion dynamics. We are interested in systems that exhibit phase transitions i.e. non-uniqueness…
Control of high-dimensional collective dynamics by deep neural feedback laws and kinetic modelling
Giacomo Albi, Sara Bicego, Dante Kalise
Modeling and control of agent-based models is twice cursed by the dimensionality of the problem, as both the number of agents and their state space dimension can be large. Even tho…
Data/moment-driven approaches for fast predictive control of collective dynamics
Giacomo Albi, Sara Bicego, Michael Herty +3
Feedback control synthesis for large-scale particle systems is reviewed in the framework of model predictive control (MPC). The high-dimensional character of collective dynamics ha…