Related papers: Optimal Estimation of Dynamically Evolving Diffusi…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems. We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying…
The problem of system identification for the Kalman filter, relying on the expectation-maximization (EM) procedure to learn the underlying parameters of a dynamical system, has largely been studied assuming that observations are sampled at…
A new application of duality relations of stochastic processes is demonstrated. Although conventional usages of the duality relations need analytical solutions for the dual processes, we here employ numerical solutions of the dual processes…
We address the problem of observation noise misspecification in Bayesian filtering of dynamical systems via recent advances in generalised Bayesian inference. Mis-match in tail decay between the true data generating process and an assumed…
This paper is concerned with the problem of distributed Kalman filtering in a network of interconnected subsystems with distributed control protocols. We consider networks, which can be either homogeneous or heterogeneous, of linear…
Optimal decision-making under partial observability requires reasoning about the uncertainty of the environment's hidden state. However, most reinforcement learning architectures handle partial observability with sequence models that have…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
This paper studies the problem of distributed state estimation (DSE) over sensor networks on matrix Lie groups, which is crucial for applications where system states evolve on Lie groups rather than vector spaces. We propose a…
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
This paper investigates ensemble Kalman inversion (EKI) for variational inverse problems with convex, potentially non-smooth regularization. While deterministic EKI and its Tikhonov-regularized variants have primarily been analyzed for…
The ensemble Kalman inversion (EKI), a recently introduced optimisation method for solving inverse problems, is widely employed for the efficient and derivative-free estimation of unknown parameters. Specifically in cases involving…
Transformer models have shown great success in natural language processing; however, their potential remains mostly unexplored for dynamical systems. In this work, we investigate the optimal output estimation problem using transformers,…
Smoothing is a specialized form of Bayesian inference for state-space models that characterizes the posterior distribution of a collection of states given an associated sequence of observations. Ramgraber et al. (2023) proposes a general…
Inverse problems are more challenging when only partial data are available in general. In this paper, we propose a two-step approach combining the extended sampling method and the ensemble Kalman filter to reconstruct an elastic rigid…
In this paper, we consider the adaptive Eulerian--Lagrangian method (ELM) for linear convection-diffusion problems. Unlike the classical a posteriori error estimations, we estimate the temporal error along the characteristics and derive a…
We address the problem of autonomous tracking and state estimation for marine vessels, autonomous vehicles, and other dynamic signals under a (structured) sparsity assumption. The aim is to improve the tracking and estimation accuracy with…
We propose an interpolation expression using the difference moment (Kolmogorov transient structural function) of the second order as the average characteristic of displacements for identifying the anomalous diffusion in complex processes…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…