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Continuous Time Echo State Networks (CTESNs) are a promising yet under-explored surrogate modeling technique for dynamical systems, particularly those governed by stiff Ordinary Differential Equations (ODEs). A key determinant of the…

Spatio-temporal data and processes are prevalent across a wide variety of scientific disciplines. These processes are often characterized by nonlinear time dynamics that include interactions across multiple scales of spatial and temporal…

Long-lead forecasting for spatio-temporal systems can often entail complex nonlinear dynamics that are difficult to specify it a priori. Current statistical methodologies for modeling these processes are often highly parameterized and thus,…

An echo state network (ESN) is a type of reservoir computer that uses a recurrent neural network with a sparsely connected hidden layer. Compared with other recurrent neural networks, one great advantage of ESN is the simplicity of its…

Echo State Networks (ESNs) are recurrent neural networks usually employed for modeling nonlinear dynamic systems with relatively ease of training. By incorporating physical laws into the training of ESNs, Physics-Informed ESNs (PI-ESNs)…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

Binary spatio-temporal data are common in many application areas. Such data can be considered from many perspectives, including via deterministic or stochastic cellular automata, where local rules govern the transition probabilities that…

Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is…

State estimation incorporates the feedback in optimization based advanced process control systems and is very important for the performance of model predictive control. We describe the extended Kalman filter, the unscented Kalman filter,…

We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the…

This paper considers the problem of data-driven prediction of partially observed systems using a recurrent neural network. While neural network based dynamic predictors perform well with full-state training data, prediction with partial…

Developing suitable approximate models for analyzing and simulating complex nonlinear systems is practically important. This paper aims at exploring the skill of a rich class of nonlinear stochastic models, known as the conditional Gaussian…

Study of dynamical systems using partial state observation is an important problem due to its applicability to many real-world systems. We address the problem by studying an echo state network (ESN) framework with partial state input with…

Prediction based on Irregularly Sampled Time Series (ISTS) is of wide concern in the real-world applications. For more accurate prediction, the methods had better grasp more data characteristics. Different from ordinary time series, ISTS is…

Neuro-inspired recurrent neural network algorithms, such as echo state networks, are computationally lightweight and thereby map well onto untethered devices. The baseline echo state network algorithms are shown to be efficient in solving…

Among the various architectures of Recurrent Neural Networks, Echo State Networks (ESNs) emerged due to their simplified and inexpensive training procedure. These networks are known to be sensitive to the setting of hyper-parameters, which…

Reservoir computing, using nonlinear dynamical systems, offers a cost-effective alternative to neural networks for complex tasks involving processing of sequential data, time series modeling, and system identification. Echo state networks…

Continuous time recurrent neural networks (CTRNN) are systems of coupled ordinary differential equations that are simple enough to be insightful for describing learning and computation, from both biological and machine learning viewpoints.…

We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms…

Echo state networks are powerful recurrent neural networks. However, they are often unstable and shaky, making the process of finding an good ESN for a specific dataset quite hard. Obtaining a superb accuracy by using the Echo State Network…