Related papers: Constructing differential equations using only a s…

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…

We propose a method for filling arbitrarily wide gaps in deterministic time series. Crucial to the method is the ability to apply Takens' theorem in order to reconstruct the dynamics underlying the time series. We introduce a functional to…

Sequentially obtained dataset usually exhibits different behavior at different data resolutions/scales. Instead of inferring from data at each scale individually, it is often more informative to interpret the data as an ensemble of time…

Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a…

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…

We present a numerical method for learning the dynamics of slow components of unknown multiscale stochastic dynamical systems. While the governing equations of the systems are unknown, bursts of observation data of the slow variables are…

For appropriately chosen weights, temporal averages in chaotic systems can be approximated as a weighted sum of averages over reference states, such as unstable periodic orbits. Under strict assumptions, such as completeness of the orbit…

We developed a novel statistical method to identify structural differences between networks characterized by structural equation models. We propose to reparameterize the model to separate the differential structures from common structures,…

Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…

We introduce a dynamical spatio-temporal model formalized as a recurrent neural network for forecasting time series of spatial processes, i.e. series of observations sharing temporal and spatial dependencies. The model learns these…

In this work, inspired in the symbolic dynamic of chaotic systems and using machine learning techniques, a control strategy for complex systems is designed. Unlike the usual methodologies based on modeling, where the control signal is…

This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…

In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Many physical systems are described by nonlinear differential equations that are too complicated to solve in full. A natural way to proceed is to divide the variables into those that are of direct interest and those that are not, formulate…

Reconstructing noise-driven nonlinear networks from time series of output variables is a challenging problem, which turns to be very difficult when nonlinearity of dynamics, strong noise impacts and low measurement frequencies jointly…

We consider systems of ordinary differential equations with multiple scales in time. In general, we are interested in the long time horizon of a slow variable that is coupled to solution components that act on a fast scale. Although the…

The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which…

Finding and sampling rare trajectories in dynamical systems is a difficult computational task underlying numerous problems and applications. In this paper we show how to construct Metropolis- Hastings Monte Carlo methods that can…

Mathematical modeling is a powerful tool for describing, predicting, and understanding complex phenomena exhibited by real-world systems. However, identifying the equations that govern a system's dynamics from experimental data remains a…