Related papers: Model-Free Prediction of Chaotic Systems Using Hig…

Reservoir computing is a best-in-class machine learning algorithm for processing information generated by dynamical systems using observed time-series data. Importantly, it requires very small training data sets, uses linear optimization,…

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…

Reservoir Computing (RC) is a simple and efficient model-free framework for forecasting the behavior of nonlinear dynamical systems from data. Here, we show that there exist commonly-studied systems for which leading RC frameworks struggle…

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…

Nonlinear stochastic modeling is useful for describing complex engineering systems. Meanwhile, neuromorphic (brain-inspired) computing paradigms are developing to tackle tasks that are challenging and resource intensive on digital…

Machine learning recently proved efficient in learning differential equations and dynamical systems from data. However, the data is commonly assumed to originate from a single never-changing system. In contrast, when modeling real-world…

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in…

Physical reservoir computing (RC) is a machine learning algorithm that employs the dynamics of a physical system to forecast highly nonlinear and chaotic phenomena. In this paper, we introduce a quantum RC system that employs the dynamics…

The prediction of complex dynamics remains an open problem across many domains of physics, where nonlinearities and multiscale interactions severely limit the reliability of conventional forecasting methods. Quantum reservoir computing…

Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…

Can a neural network trained by the time series of system A be used to predict the evolution of system B? This problem, knowing as transfer learning in a broad sense, is of great importance in machine learning and data mining, yet has not…

Reservoir computing is a recently introduced machine learning paradigm that has been shown to be well-suited for the processing of spatiotemporal data. Rather than training the network node connections and weights via backpropagation in…

Time-series forecasting is a challenging problem that traditionally requires specialized models custom-trained for the specific task at hand. Recently, inspired by the success of large language models, foundation models pre-trained on vast…

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…

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…

We propose a dual-channel reservoir-computing scheme for inferring the dynamics of two distinct chaotic systems with a single machine. By augmenting a standard reservoir with a system-label channel and a parameter-control channel, the…

Reservoir computing aims to achieve high-performance and low-cost machine learning with a dynamical system as a reservoir. However, in general, there are almost no theoretical guidelines for its high-performance or optimality. Therefore,…

Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…

Forecasting high-dimensional spatiotemporal systems remains computationally challenging for recurrent neural networks (RNNs) and long short-term memory (LSTM) models due to gradient-based training and memory bottlenecks. Reservoir Computing…

Forecasting nonlinear time series with multi-scale temporal structures remains a central challenge in complex systems modeling. We present a novel reservoir computing framework that combines delay embedding with random Fourier feature (RFF)…