212 citations · 454 across the 29 of their papers we have counts for
14 papers · 1 filter
Higher-Order Mean-Field Control Barrier Functions
Levon Nurbekyan, Samy Wu Fung
Mean-field control barrier functions (MF-CBFs) enforce swarm safety through constraints on the agents' distribution. Previous formulations, including applications to stochastic cov…
A primal-dual price-optimization method for computing equilibrium prices in mean-field games models
Xu Wang, Samy Wu Fung, Levon Nurbekyan
We develop a simple yet efficient Lagrangian method for computing equilibrium prices in a mean-field game price-formation model. We prove that equilibrium prices are optimal in ter…
Mean-Field Control Barrier Functions: A Framework for Real-Time Swarm Control
Samy Wu Fung, Levon Nurbekyan
Control Barrier Functions (CBFs) are an effective methodology to ensure safety and performative efficacy in real-time control applications such as power systems, resource allocatio…
Kernel Expansions for High-Dimensional Mean-Field Control with Non-local Interactions
Alexander Vidal, Samy Wu Fung, Stanley Osher +2
Mean-field control (MFC) problems aim to find the optimal policy to control massive populations of interacting agents. These problems are crucial in areas such as economics, physic…
Monotone inclusion methods for a class of second-order non-potential mean-field games
Levon Nurbekyan, Siting Liu, Yat Tin Chow
We propose a monotone splitting algorithm for solving a class of second-order non-potential mean-field games. Following [Achdou, Capuzzo-Dolcetta, "Mean Field Games: Numerical Meth…
A note on the convergence of the monotone inclusion version of the primal-dual hybrid gradient algorithm
Levon Nurbekyan
The note contains a direct extension of the Chambolle and Pock convergence proof of the primal-dual hybrid gradient (PDHG) algorithm to the case of monotone inclusions.
Adaptive Preconditioned Gradient Descent with Energy
Hailiang Liu, Levon Nurbekyan, Xuping Tian +1
We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied…
Taming Hyperparameter Tuning in Continuous Normalizing Flows Using the JKO Scheme
Alexander Vidal, Samy Wu Fung, Luis Tenorio +2
A normalizing flow (NF) is a mapping that transforms a chosen probability distribution to a normal distribution. Such flows are a common technique used for data generation and dens…
Efficient Natural Gradient Descent Methods for Large-Scale PDE-Based Optimization Problems
Levon Nurbekyan, Wanzhou Lei, Yunan Yang
We propose efficient numerical schemes for implementing the natural gradient descent (NGD) for a broad range of metric spaces with applications to PDE-based optimization problems.…
A Neural Network Approach for High-Dimensional Optimal Control Applied to Multi-Agent Path Finding
Derek Onken, Levon Nurbekyan, Xingjian Li +3
We propose a neural network approach that yields approximate solutions for high-dimensional optimal control problems and demonstrate its effectiveness using examples from multi-age…
A Neural Network Approach Applied to Multi-Agent Optimal Control
Derek Onken, Levon Nurbekyan, Xingjian Li +3
We propose a neural network approach for solving high-dimensional optimal control problems. In particular, we focus on multi-agent control problems with obstacle and collision avoi…
Splitting methods for a class of non-potential mean field games
Siting Liu, Levon Nurbekyan
We extend the methods from Nurbekyan, Saude "Fourier approximation methods for first-order nonlocal mean-field games" [Port. Math. 75 (2018), no. 3-4] and Liu, Jacobs, Li, Nurbekya…
Computational methods for nonlocal mean field games with applications
Siting Liu, Matthew Jacobs, Wuchen Li +2
We introduce a novel framework to model and solve mean-field game systems with nonlocal interactions. Our approach relies on kernel-based representations of mean-field interactions…
No-collision Transportation Maps
Levon Nurbekyan, Alexander Iannantuono, Adam M. Oberman
Transportation maps between probability measures are critical objects in numerous areas of mathematics and applications such as PDE, fluid mechanics, geometry, machine learning, co…