Related papers: Comparison of continuous and discrete-time data-ba…
We focus on variational inference in dynamical systems where the discrete time transition function (or evolution rule) is modelled by a Gaussian process. The dominant approach so far has been to use a factorised posterior distribution,…
In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show…
Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…
Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…
Mechanistic modelling of animal movement is often formulated in discrete time despite problems with scale invariance, such as handling irregularly timed observations. A natural solution is to formulate in continuous time, yet uptake of this…
In this article, we consider abstract linear conservative systems and their time-discrete counterparts. Our main result is a representation formula expressing solutions of the continuous model through the solution of the corresponding…
Stochastic differential equations (SDEs) provide a flexible framework for modeling temporal dynamics in partially observed systems. A central task is to calibrate such models from data, which requires inferring latent trajectories and…
We consider nonparametric invariant density and drift estimation for a class of multidimensional degenerate resp. hypoelliptic diffusion processes, so-called stochastic damping Hamiltonian systems or kinetic diffusions, under anisotropic…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Data-driven control offers a powerful alternative to traditional model-based methods, particularly when accurate system models are unavailable or prohibitively complex. While existing data-driven control methods primarily aim to construct…
We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settings are analyzed: hidden…
This paper develops computationally feasible methods for estimating random effects models in the context of regression modelling of multiple independent time series of discrete valued counts in which there is serial dependence. Given…
We present an algorithm to evaluate the large deviation functions associated to history-dependent observables. Instead of relying on a time discretisation procedure to approximate the dynamics, we provide a direct continuous-time algorithm,…
In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization,…
This paper revisits the classical notion of sampling in the setting of real-time temporal logics for the modeling and analysis of systems. The relationship between the satisfiability of Metric Temporal Logic (MTL) formulas over…
Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…
In this paper, we study the estimation of drift and diffusion coefficients in a two dimensional system of N interacting particles modeled by a degenerate stochastic differential equation. We consider both complete and partial observation…
Modeling an unknown dynamical system is crucial in order to predict the future behavior of the system. A standard approach is training recurrent models on measurement data. While these models typically provide exact short-term predictions,…
We consider the problem of estimating states and parameters in a model based on a system of coupled stochastic differential equations, based on noisy discrete-time data. Special attention is given to nonlinear dynamics and state-dependent…
On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The…