Related papers: Efficient Spectral Differentiation in Grid-Based C…
This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-point-based…
This paper deals with the problem of efficient sampling from a stochastic differential equation, given the drift function and the diffusion matrix. The proposed approach leverages a recent model for probabilities \cite{rudi2021psd} (the…
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, samples are compared and only those which pass a goodness-of-fit test are used to…
In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…
We propose a novel non-parametric learning paradigm for the identification of drift and diffusion coefficients of multi-dimensional non-linear stochastic differential equations, which relies upon discrete-time observations of the state. The…
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 present a new strategy to approximate the global solution of the Fokker-Planck equation efficiently in higher dimensions and show its convergence. The main ingredients are the Euler scheme to solve the associated stochastic differential…
In this paper, we propose a novel method to approximate the mean field stochastic differential equation by means of approximating the density function via Fokker-Planck equation. We construct a well-posed truncated Fokker-Planck equation…
General Stochastic Hybrid Systems (GSHS) have been formulated to represent various types of uncertainties in hybrid dynamical systems. In this paper, we propose computational techniques for Bayesian estimation of GSHS. In particular, the…
The steady state of the Fokker-Planck equation corresponding to a density dependent one-step process is approximated by a suitable normal distribution. Starting from the master equations of the process, written in terms of the time…
The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable…
This paper presents a new approach for filter design based on stochastic distances and tests between distributions. A window is defined around each pixel, overlapping samples are compared and only those which pass a goodness-of-fit test are…
Many stochastic differential equations in various applications like coupled neuronal oscillators are driven by time-periodic forces. In this paper, we extend several data-driven computational tools from autonomous Fokker-Planck equation to…
A spectral method is developed for the direct solution of linear ordinary differential equations with variable coefficients. The method leads to matrices which are almost banded, and a numerical solver is presented that takes O(m^2n)…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
Spectral independence is a recently-developed framework for obtaining sharp bounds on the convergence time of the classical Glauber dynamics. This new framework has yielded optimal $O(n \log n)$ sampling algorithms on bounded-degree graphs…
We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two types of state…
This paper deals with state estimation of stochastic models with linear state dynamics, continuous or discrete in time. The emphasis is laid on a numerical solution to the state prediction by the time-update step of the grid-point-based…
State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter,…
Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the robustness of these patterns with respect to noise is one of the key open questions in…