Related papers: Filtering Dynamical Systems Using Observations of …
The method of choice for integrating the time-dependent Fokker-Planck equation in high-dimension is to generate samples from the solution via integration of the associated stochastic differential equation. Here, we study an alternative…
Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…
Data assimilation (DA) is a key component of many forecasting models in science and engineering. DA allows one to estimate better initial conditions using an imperfect dynamical model of the system and noisy/sparse observations available…
Significant efforts have gone into the development of statistical models for analyzing data in the form of networks, such as social networks. Most existing work has focused on modeling static networks, which represent either a single time…
The Ensemble Kalman Filter (EnKF) has achieved great successes in data assimilation in atmospheric and oceanic sciences, but its failure in convergence to the right filtering distribution precludes its use for uncertainty quantification. We…
We study a Fokker-Planck equation modelling the firing rates of two interacting populations of neurons. This model arises in computational neuroscience when considering, for example, bistable visual perception problems and is based on a…
An Ensemble Kalman Filter (EnKF, the predictor) is used make a large change in the state, followed by a Particle Filer (PF, the corrector) which assigns importance weights to describe non-Gaussian distribution. The weights are obtained by…
Estimation of a dynamical system's latent state subject to sensor noise and model inaccuracies remains a critical yet difficult problem in robotics. While Kalman filters provide the optimal solution in the least squared sense for linear and…
We develop a general framework for state estimation in systems modeled with noise-polluted continuous time dynamics and discrete time noisy measurements. Our approach is based on maximum likelihood estimation and employs the calculus of…
The ensemble Kalman filter (EnKF) is widely used for data assimilation in high-dimensional systems, but its performance often deteriorates for strongly nonlinear dynamics due to the structural mismatch between the Kalman update and the…
We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a…
Over the years data assimilation methods have been developed to obtain estimations of uncertain model parameters by taking into account a few observations of a model state. The most reliable methods of MCMC are computationally expensive.…
Many recent advances in sequential assimilation of data into nonlinear high-dimensional models are modifications to particle filters which employ efficient searches of a high-dimensional state space. In this work, we present a complementary…
For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the…
We consider dynamical systems evolving near an equilibrium statistical state where the interest is in modelling long term behavior that is consistent with thermodynamic constraints. We adjust the distribution using an entropy-optimizing…
This paper is concerned with the convergence and long-term stability analysis of the feedback particle filter (FPF) algorithm. The FPF is an interacting system of $N$ particles where the interaction is designed such that the empirical…
Data assimilation plays a key role in large-scale atmospheric weather forecasting, where the state of the physical system is estimated from model outputs and observations, and is then used as initial condition to produce accurate future…
The purpose of this paper is to describe the feedback particle filter algorithm for problems where there are a large number ($M$) of non-interacting agents (targets) with a large number ($M$) of non-agent specific observations…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…
Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can…