Related papers: Dynamic system classifier
Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…
Learning continuous-time stochastic dynamics is a fundamental and essential problem in modeling sporadic time series, whose observations are irregular and sparse in both time and dimension. For a given system whose latent states and…
Understanding how external stimuli are encoded in distributed neural activity is of significant interest in clinical and basic neuroscience. To address this need, it is essential to develop analytical tools capable of handling limited data…
Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse…
Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at…
Dynamical sampling refers to a class of problems in which space-time samples are taken from a signal evolving under an underlying dynamical system. The goal is to use these samples to recover relevant information about the system, such as…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…
Learning complex trajectories from demonstrations in robotic tasks has been effectively addressed through the utilization of Dynamical Systems (DS). State-of-the-art DS learning methods ensure stability of the generated trajectories;…
Causal representation learning promises to extend causal models to hidden causal variables from raw entangled measurements. However, most progress has focused on proving identifiability results in different settings, and we are not aware of…
We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with…
The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
Computer simulations have become an important tool across the biomedical sciences and beyond. For many important problems several different models or hypotheses exist and choosing which one best describes reality or observed data is not…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
Encoding a sequence of observations is an essential task with many applications. The encoding can become highly efficient when the observations are generated by a dynamical system. A dynamical system imposes regularities on the observations…
We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or…
There is a whole range of emergent phenomena in non-equilibrium behaviors can be well described by a set of stochastic differential equations. Inspired by an insight gained during our study of robustness and stability in phage lambda…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…