9 papers
Well-posedness and Hurst parameter estimation for fluid equations driven by fractional transport noise
Alexandra Blessing Neamtu, Dan Crisan, Oana Lang
We study a two-dimensional incompressible vorticity equation on the torus driven by transport-type fractional Brownian noise with Hurst parameter . The model capture…
Data assimilation using a global Girsanov nudged particle filter
Maneesh Kumar Singh, Joshua Hope-Collins, Colin J. Cotter +1
We present a particle filtering algorithm for stochastic models on infinite dimensional state space, making use of Girsanov perturbations to nudge the ensemble of particles into re…
A localized particle filter for geophysical data assimilation
Dan Crisan, Eliana Fausti
Particle filters are computational techniques for estimating the state of dynamical systems by integrating observational data with model predictions. This work introduces a class o…
A uniform particle approximation to the Navier-Stokes-alpha models in three dimensions with advection noise
Filippo Giovagnini, Dan Crisan
In this work, we investigate a system of interacting particles governed by a set of stochastic differential equations. Our main goal is to rigorously demonstrate that the empirical…
Bayesian inference for geophysical fluid dynamics using generative models
Alexander Lobbe, Dan Crisan, Oana Lang
Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive ca…
A uniform point vortex approximation for the solution of the two-dimensional Navier Stokes equation with transport noise
Filippo Giovagnini, Dan Crisan
We study a model of interacting particles represented by a system of N stochastic differential equations. We establish that the mollified empirical distribution of the system conve…
Generative Modelling of Stochastic Rotating Shallow Water Noise
Dan Crisan, Oana Lang, Alexander Lobbe
In recent work, the authors have developed a generic methodology for calibrating the noise in fluid dynamics stochastic partial differential equations where the stochasticity was i…
Global solutions for stochastically controlled fluid dynamics models
Dan Crisan, Oana Lang
For a class of evolution equations that possibly have only local solutions, we introduce a stochastic component that ensures that the solutions of the corresponding stochastically…
Data assimilation for the stochastic Camassa-Holm equation using particle filtering: a numerical investigation
Colin John Cotter, Dan Crisan, Maneesh Kumar Singh
In this study, we explore data assimilation for the Stochastic Camassa-Holm equation through the application of the particle filtering framework. Specifically, our approach integra…