26 papers
On the diffusive-mean field limit of a kinetic weakly interacting particle system
Raphaël Gastaldello, Grigorios A. Pavliotis, Gabriel Stoltz +1
We study the joint diffusive-mean field limit for a system of weakly interacting kinetic Langevin dynamics, extending the results of Delgadino, Gvalani and Pavliotis (Arch. Ration.…
Cluster formation for weakly interacting kinetic Langevin dynamics
Benedict Leimkuhler, René Lohmann, Grigorios A. Pavliotis +1
In this paper, we study the formation of clusters for stochastic interacting particle systems (IPS) that interact through short-range attractive potentials in a periodic domain. We…
A theory of generalised coordinates for stochastic differential equations
Lancelot Da Costa, Nathaël Da Costa, Conor Heins +5
Stochastic differential equations are ubiquitous modelling tools in physics and the sciences. In most modelling scenarios, random fluctuations driving dynamics or motion have some…
Diffusion Models Preferentially Memorize Prototypical Examples or: Why Does My Diffusion Model Love Slop?
Marta Aparicio Rodriguez, Anastasia Borovykh, Grigorios A. Pavliotis +1
Generative models have a persistent limitation: their tendency to memorize training data can create legal liabilities and erode creative diversity. Understanding which samples are…
Recursive Maximum Likelihood Estimation for Interacting Particle Systems using Virtual Particles
Louis Sharrock, Nikolas Kantas, Grigorios A. Pavliotis
We study recursive maximum likelihood estimation for stochastic interacting particle systems based on continuous observation of a single particle. In this regime, consistent estima…
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…