161 citations · 2k across the 112 of their papers we have counts for
7 papers · 1 filter
Neural network approaches for variance reduction in fluctuation formulas
Grigorios Pavliotis, Renato Spacek, Gabriel Stoltz +1
We propose a method utilizing physics-informed neural networks (PINNs) to solve Poisson equations that serve as control variates in the computation of transport coefficients via fl…
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…
Approximating particle-based clustering dynamics by stochastic PDEs
Nathalie Wehlitz, Mohsen Sadeghi, Alberto Montefusco +3
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membr…
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…
Stability of stationary states for mean field models with multichromatic interaction potentials
Benedetta Bertoli, Benjamin D. Goddard, Grigorios A. Pavliotis
We consider weakly interacting diffusions on the torus, for multichromatic interaction potentials. We consider interaction potentials that are not H-stable, leading to phase transi…
Bayesian Nonparametric Inference in McKean-Vlasov models
Richard Nickl, Grigorios A. Pavliotis, Kolyan Ray
We consider nonparametric statistical inference on a periodic interaction potential from noisy discrete space-time measurements of solutions of the nonlinear McKean-Vla…