Related papers: Non-Factorised Variational Inference in Dynamical …

This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…

Gaussian process regression is increasingly applied for learning unknown dynamical systems. In particular, the implicit quantification of the uncertainty of the learned model makes it a promising approach for safety-critical applications.…

We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…

In this paper we develop a novel approach for estimating large and sparse dynamic factor models using variational inference, also allowing for missing data. Inspired by Bayesian variable selection, we apply slab-and-spike priors onto the…

We present a straightforward and efficient way to control unstable robotic systems using an estimated dynamics model. Specifically, we show how to exploit the differentiability of Gaussian Processes to create a state-dependent linearized…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

We study a class of stochastic evolution equations with a dissipative forcing nonlinearity and additive noise. The noise is assumed to satisfy rather general assumptions about the form of the covariance function; our framework covers…

This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…

In this paper, the optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the…

Data-driven control of nonlinear systems with rigorous guarantees is a challenging problem as it usually calls for nonconvex optimization and requires often knowledge of the true basis functions of the system dynamics. To tackle these…

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…

Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…

We present a general framework for classifying partially observed dynamical systems based on the idea of learning in the model space. In contrast to the existing approaches using model point estimates to represent individual data items, we…

A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…

The appropriate description of fluctuations within the framework of evolutionary game theory is a fundamental unsolved problem in the case of finite populations. The Moran process recently introduced into this context [Nowak et al., Nature…

Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…

We introduce a simulation-based, amortised Bayesian inference scheme to infer the parameters of random walks. Our approach learns the posterior distribution of the walks' parameters with a likelihood-free method. In the first step a graph…

We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems…

Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…

The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent…