Publications de Grigorios A. Pavliotis

A Method of Moments Estimator for Interacting Particle Systems and their Mean Field Limit

We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...

Siam Publications2024

Drift Estimation of Multiscale Diffusions Based on Filtered Data

Assyr Abdulle, Giacomo Garegnani, Andrea Zanoni, Grigorios A. Pavliotis

We study the problem of drift estimation for two-scale continuous time series. We set ourselves in the framework of overdamped Langevin equations, for which a single-scale surrogate homogenized equation exists. In this setting, estimating the drift coeffic ...

2023

Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations

Assyr Abdulle, Gilles Vilmart, Grigorios A. Pavliotis

In this paper, we propose a new approach for sampling from probability measures in, possibly, high-dimensional spaces. By perturbing the standard overdamped Langevin dynamics by a suitable Stratonovich perturbation that preserves the invariant measure of t ...

2019

Spectral methods for multiscale stochastic differential equations

Assyr Abdulle, Grigorios A. Pavliotis

This paper presents a new method for the solution of multiscale stochastic differential equations at the diffusive time scale. In contrast to averaging-based methods, e.g., the heterogeneous multiscale method (HMM) or the equation-free method, which rely o ...

2017

Data-driven coarse graining in action: Modeling and prediction of complex systems

Sebastian Krumscheid, Grigorios A. Pavliotis

In many physical, technological, social, and economic applications, one is commonly faced with the task of estimating statistical properties, such as mean first passage times of a temporal continuous process, from empirical data (experimental observations) ...

Amer Physical Soc2015

Numerical methods for stochastic partial differential equations with multiple scales

Assyr Abdulle, Grigorios A. Pavliotis

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...

2012