相关论文: Continuous time limit of the stochastic ensemble K…

Stochastic interpolants offer a robust framework for continuously transforming samples between arbitrary data distributions, holding significant promise for generative modeling. Despite their potential, rigorous finite-time convergence…

We propose an approach based on function evaluations and Bayesian inference to extract higher-order differential information of objective functions {from a given ensemble of particles}. Pointwise evaluation $\{V(x^i)\}_i$ of some potential…

The ensemble random forest filter (ERFF) is presented as an alternative to the ensemble Kalman filter (EnKF) for the purpose of inverse modeling. The EnKF is a data assimilation approach that forecasts and updates parameter estimates…

Stochastic contraction analysis is a recently developed tool for studying the global stability properties of nonlinear stochastic systems, based on a differential analysis of convergence in an appropriate metric. To date, stochastic…

Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…

This paper presents a computationally fast algorithm for estimating, both, the system and observation noise covariances of nonlinear dynamics, that can be used in an ensemble Kalman filtering framework. The new method is a modification of…

This paper extends the ensemble Kalman filter (EnKF) for inverse problems to identify trending model coefficients. This is done by repeatedly inflating the ensemble while maintaining the mean of the particles. As a benchmark serves a…

We rigorously derive novel error bounds for extended dynamic mode decomposition (EDMD) to approximate the Koopman operator for discrete- and continuous time (stochastic) systems; both for i.i.d. and ergodic sampling under non-restrictive…

In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is refined, the estimate…

Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method of order N and collocation method of order M.…

Randomized algorithms exploit stochasticity to reduce computational complexity. One important example is random feature regression (RFR) that accelerates Gaussian process regression (GPR). RFR approximates an unknown function with a random…

This paper focuses on inverse problems to identify parameters by incorporating information from measurements. These generally ill-posed problems are formulated here in a probabilistic setting based on Bayes's theorem because it leads to a…

This paper is concerned with the mathematical analysis of continuous time Ensemble Kalman Filters (EnKBFs) and their mean field limit in an infinite dimensional setting. The signal is determined by a nonlinear Stochastic Partial…

Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they…

Despite the cheap availability of computing resources enabling faster Monte Carlo simulations, the potential benefits of particle filtering in revealing accurate statistical information on the imprecisely known model parameters or modeling…

We consider the problem of inference for the states and parameters of a continuous-time multitype branching process from partially observed time series data. Exact inference for this class of models, typically using sequential Monte Carlo,…

We propose a new class of filtering and smoothing methods for inference in high-dimensional, nonlinear, non-Gaussian, spatio-temporal state-space models. The main idea is to combine the ensemble Kalman filter and smoother, developed in the…

We present a stochastic predictive controller for discrete time linear time invariant systems under incomplete state information. Our approach is based on a suitable choice of control policies, stability constraints, and employment of a…

Estimating the statistics of the state of a dynamical system, from partial and noisy observations, is both mathematically challenging and finds wide application. Furthermore, the applications are of great societal importance, including…

In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…