Related papers: Fokker-Planck particle systems for Bayesian infere…
A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…
A new computational method is presented for study suspensions of charged soft particles undergoing fluctuating hydrodynamic and electrostatic interactions. The proposed model is appropriate for polymers, proteins and porous particles…
We present a field theoretic approach to capture the motion of a particle with dry friction for one- and two-dimensional diffusive particles, and further expand the framework for two-dimensional active Brownian particles. Starting with the…
We present a scalable approach to performing approximate fully Bayesian inference in generic state space models. The proposed method is an alternative to particle MCMC that provides fully Bayesian inference of both the dynamic latent states…
In these lecture notes, we explore the mathematical preliminaries and foundational concepts that connect stochastic processes with partial differential equations. We begin by investigating Brownian motion, which serves as a model for random…
The Fokker-Planck (FP) equation is a linear partial differential equation which governs the temporal and spatial evolution of the probability density function (PDF) associated with the response of stochastic dynamical systems. An exact…
We study the nonlinear Fokker-Planck equation on graphs, which is the gradient flow in the space of probability measures supported on the nodes with respect to the discrete Wasserstein metric. The energy functional driving the gradient flow…
The behavior of a heavy tagged intruder immersed in a bath of particles evolving under ballistic annihilation dynamics is investigated. The Fokker-Planck equation for this system is derived and the peculiarities of the corresponding…
Data assimilation (DA) provides a general framework for estimation in dynamical systems based on the concepts of Bayesian inference. This constitutes a common basis for the different linear and nonlinear filtering and smoothing techniques…
We consider a class of nonlinear partial-differential equations, including the spatially homogeneous Fokker-Planck-Landau equation for Maxwell (or pseudo-Maxwell) molecules. Continuing the work of Fontbona-Gu\'erin-M\'el\'eard, we propose a…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
The Fokker-Planck equation for a heavy particle in a granular fluid is derived from the Liouville equation. The host fluid is assumed to be in its homogeneous cooling state and all interactions are idealized as smooth, inelastic hard…
Solving the stationary nonlinear Fokker-Planck equations is important in applications and examples include the Poisson-Boltzmann equation and the two layer neural networks. Making use of the connection between the interacting particle…
The relaxation towards equilibrium of systems with long range interactions is not yet fully understood. As a step towards such a comprehension, we propose the study of the dynamical equilibrium fluctuations in a model system with long range…
We describe a novel approach to statistical learning from particles tracked while moving in a random environment. The problem consists in inferring properties of the environment from recorded snapshots. We consider here the case of a fluid…
For stochastic systems with discrete time delay, the Fokker-Planck equation (FPE) of the one-time probability density function (PDF) does not provide a complete, self-contained probabilistic description. It explicitly involves the two-time…
It is well known that path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers.…
A system of N Brownian particles suspended in a nonuniform heat bath is treated as a thermodynamic system whith internal degrees of freedom, in this case their velocities and coordinates. Applying the scheme of non-equilibrium…
Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion,…
We consider Bayesian inference for large scale inverse problems, where computational challenges arise from the need for repeated evaluations of an expensive forward model. This renders most Markov chain Monte Carlo approaches infeasible,…