Related papers: Dynamical modelling of superstatistical complex sy…

We present a framework for constructing physics and causally constrained neural models of turbulent dynamical systems from data. We first formulate a finite-time flow map with strict energy-preserving nonlinearities for stable modeling of…

Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…

We present an analytical scheme, easily implemented numerically, to generate synthetic Gaussian turbulent flows by using a linear Langevin equation, where the noise term acts as a stochastic stirring force. The characteristic parameters of…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

To understand how neural networks process information, it is important to investigate how neural network dynamics varies with respect to different stimuli. One challenging task is to design efficient statistical approaches to analyze…

The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often…

Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory…

The probability distributions, as well as the mean values of stochastic currents and fluxes, associated with a driven Langevin process, provide a good and topologically protected measure of how far a stochastic system is driven out of…

Experimentally observed networks of interacting dynamical systems are inferred from recorded multivariate time series by evaluating a statistical measure of dependence, usually the cross-correlation coefficient, or mutual information. These…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

A new class of models, named dynamic quantile linear models, is presented. It combines dynamic linear models with distribution free quantile regression producing a robust statistical method. Bayesian inference for dynamic quantile linear…

This paper presents a new robust data-driven predictive control scheme for unknown linear time-invariant systems by using input-state-output or input-output data based on whether the state is measurable. To remove the need for the…

Dynamical models of cognition play an increasingly important role in driving theoretical and experimental research in psychology. Therefore, parameter estimation, model analysis and comparison of dynamical models are of essential…

Quantitatively modeling the trajectories and behavior of pedestrians walking in crowds is an outstanding fundamental challenge deeply connected with the physics of flowing active matter, from a scientific point of view, and having societal…

This paper generalises dynamic factor models for multidimensional dependent data. In doing so, it develops an interpretable technique to study complex information sources ranging from repeated surveys with a varying number of respondents to…

Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures.…

In this paper, we characterize the synchronization phenomenon of hyperchaotic scalar non-linear delay dynamics in a fully-developed chaos regime. Our results rely on the observation that, in that regime, the stationary statistical…

The evolution of sequence modeling architectures, from recurrent neural networks and convolutional models to Transformers and structured state-space models, reflects ongoing efforts to address the diverse temporal dependencies inherent in…

Diffusion models have quickly risen in popularity for their ability to model complex distributions and perform effective posterior sampling. Unfortunately, the iterative nature of these generative models makes them computationally expensive…