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We demonstrate a data-driven technique for adaptive control in dynamical systems that exploits the reservoir computing method. We show that a reservoir computer can be trained to predict a system parameter from the time series data.…

Transformers have become the dominant architecture for sequence modeling tasks such as natural language processing or audio processing, and they are now even considered for tasks that are not naturally sequential such as image…

Transformers have achieved superior performances in many tasks in natural language processing and computer vision, which also triggered great interest in the time series community. Among multiple advantages of Transformers, the ability to…

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…

Machine learning techniques offer an effective approach to modeling dynamical systems solely from observed data. However, without explicit structural priors -- built-in assumptions about the underlying dynamics -- these techniques typically…

In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…

Recurrent Neural Networks were, until recently, one of the best ways to capture the timely dependencies in sequences. However, with the introduction of the Transformer, it has been proven that an architecture with only attention-mechanisms…

Deep learning models, particularly Transformers, have achieved impressive results in various domains, including time series forecasting. While existing time series literature primarily focuses on model architecture modifications and data…

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle large systems. Its implementation, however, often requires full state-vector measurements and…

Model extrapolation to unseen flow is one of the biggest challenges facing data-driven turbulence modeling, especially for models with high dimensional inputs that involve many flow features. In this study we review previous efforts on…

Neural networks have in recent years shown promise for helping software engineers write programs and even formally verify them. While semantic information plays a crucial part in these processes, it remains unclear to what degree popular…

Reservoir computing is a machine learning approach that can generate a surrogate model of a dynamical system. It can learn the underlying dynamical system using fewer trainable parameters and hence smaller training data sets than competing…

We present a novel, model-free, and data-driven methodology for controlling complex dynamical systems into previously unseen target states, including those with significantly different and complex dynamics. Leveraging a parameter-aware…

Non-stationary sequences arise naturally in control, forecasting, and decision-making. The data-generating process shifts at unknown times, and models must detect the change, discard or downweight obsolete evidence, and adapt to new…

We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…

Multimodal data collected from the real world are often imperfect due to missing modalities. Therefore multimodal models that are robust against modal-incomplete data are highly preferred. Recently, Transformer models have shown great…

Models of complex dynamical systems like the Earth's climate often involve large numbers of uncertain parameters. Comprehensive exploration of the parameter space is typically prohibitive due to excessive computational costs. Systematic…

We propose and demonstrate a nonlinear control method that can be applied to unknown, complex systems where the controller is based on a type of artificial neural network known as a reservoir computer. In contrast to many modern…

The prediction of stochastic dynamical systems and the capture of dynamical behaviors are profound problems. In this article, we propose a data-driven framework combining Reservoir Computing and Normalizing Flow to study this issue, which…

Transformer architecture has widespread applications, particularly in Natural Language Processing and computer vision. Recently Transformers have been employed in various aspects of time-series analysis. This tutorial provides an overview…