Related papers: Hybrid Forecasting of Chaotic Processes: Using Mac…

We consider the commonly encountered situation (e.g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous…

The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

We scrutinize the use of machine learning, based on reservoir computing, to build data-driven effective models of multiscale chaotic systems. We show that, for a wide scale separation, machine learning generates effective models akin to…

In numerical modeling of the Earth System, many processes remain unknown or ill represented (let us quote sub-grid processes, the dependence to unknown latent variables or the non-inclusion of complex dynamics in numerical models) but…

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

Scientific analysis often relies on the ability to make accurate predictions of a system's dynamics. Mechanistic models, parameterized by a number of unknown parameters, are often used for this purpose. Accurate estimation of the model…

Chaos and unpredictability are traditionally synonymous, yet large-scale machine learning methods recently have demonstrated a surprising ability to forecast chaotic systems well beyond typical predictability horizons. However, recent works…

Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…

This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…

To understand and predict the performance of scientific applications, several analytical and machine learning approaches have been proposed, each having its advantages and disadvantages. In this paper, we propose and validate a hybrid…

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…

To operate process engineering systems in a safe and reliable manner, predictive models are often used in decision making. In many cases, these are mechanistic first principles models which aim to accurately describe the process. In…

In applications of dynamical systems, situations can arise where it is desired to predict the onset of synchronization as it can lead to characteristic and significant changes in the system performance and behaviors, for better or worse. In…

We propose a physics-aware machine learning method to time-accurately predict extreme events in a turbulent flow. The method combines two radically different approaches: empirical modelling based on reservoir computing, which learns the…

Reliable prediction of large chaotic sytems in the short to middle time range is of interest in a number of fields, including climate, ecology, seismology, and economics. In this paper, results from chaos theory, and statistical theory are…

Complex numerical weather prediction models incorporate a variety of physical processes, each described by multiple alternative physical schemes with specific parameters. The selection of the physical schemes and the choice of the…

We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two…

Two recent papers on prediction of chaotic systems, one on multi-view embedding1 , and the second on prediction in projection2 provide empirical evidence to support particular prediction methods for chaotic systems. Multi-view embedding1 is…

To predict the future evolution of dynamical systems purely from observations of the past data is of great potential application. In this work, a new formulated paradigm of reservoir computing is proposed for achieving model-free…