212 citations · 454 across the 29 of their papers we have counts for
37 papers
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…
Mean-field control barrier functions for stochastic multi-agent systems
Cinzia Tomaselli, Gian Carlo Maffettone, Samy Wu Fung +2
Many applications involving multi-agent systems require fulfilling safety constraints. Control barrier functions offer a systematic framework to enforce forward invariance of safet…
Differentiating through Stochastic Differential Equations: A Primer
Rishi Leburu, Levon Nurbekyan, Lars Ruthotto
Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investig…
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…
Applications of No-Collision Transportation Maps in Manifold Learning
Elisa Negrini, Levon Nurbekyan
In this work, we investigate applications of no-collision transportation maps introduced in [Nurbekyan et. al., 2020] in manifold learning for image data. Recently, there has been…
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…
A numerical algorithm for inverse problem from partial boundary measurement arising from mean field game problem
Yat Tin Chow, Samy Wu Fung, Siting Liu +2
In this work, we consider a novel inverse problem in mean-field games (MFG). We aim to recover the MFG model parameters that govern the underlying interactions among the population…
Random Features for High-Dimensional Nonlocal Mean-Field Games
Sudhanshu Agrawal, Wonjun Lee, Samy Wu Fung +1
We propose an efficient solution approach for high-dimensional nonlocal mean-field game (MFG) systems based on the Monte Carlo approximation of interaction kernels via random featu…
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.…
Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures
Yunan Yang, Levon Nurbekyan, Elisa Negrini +2
We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for e…
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…
Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games
Alex Tong Lin, Samy Wu Fung, Wuchen Li +2
We present APAC-Net, an alternating population and agent control neural network for solving stochastic mean field games (MFGs). Our algorithm is geared toward high-dimensional inst…
How to train your neural ODE: the world of Jacobian and kinetic regularization
Chris Finlay, Jörn-Henrik Jacobsen, Levon Nurbekyan +1
Training neural ODEs on large datasets has not been tractable due to the necessity of allowing the adaptive numerical ODE solver to refine its step size to very small values. In pr…
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…
A Machine Learning Framework for Solving High-Dimensional Mean Field Game and Mean Field Control Problems
Lars Ruthotto, Stanley Osher, Wuchen Li +2
Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of a…
Fourier Approximation Methods for First-Order Nonlocal Mean-Field Games
Levon Nurbekyan, Joao Saude
In this note, we develop Fourier approximation methods for the solutions of first-order nonlocal mean-field games (MFG) systems. Using Fourier expansion techniques, we approximate…