Related papers: Data-driven Reconstruction of Nonlinear Dynamics f…

Echo state network (ESN), a kind of recurrent neural networks, consists of a fixed reservoir in which neurons are connected randomly and recursively and obtains the desired output only by training output connection weights. First-order…

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and non-stationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently…

The real-time prediction of chaotic systems requires a nonlinear-reduced order model (ROM) to forecast the dynamics, and a stream of data from sensors to update the ROM. Data-driven ROMs are typically built with a two-step strategy: data…

Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear…

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…

We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…

Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in…

We propose a physics-informed Echo State Network (ESN) to predict the evolution of chaotic systems. Compared to conventional ESNs, the physics-informed ESNs are trained to solve supervised learning tasks while ensuring that their…

To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…

Deriving precise system dynamic models through traditional numerical methods is often a challenging endeavor. The performance of Model Predictive Control is heavily contingent on the accuracy of the system dynamic model. Consequently, this…

Learning predictive models from observations using deep neural networks (DNNs) is a promising new approach to many real-world planning and control problems. However, common DNNs are too unstructured for effective planning, and current…

This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…

An approach to the time-accurate prediction of chaotic solutions is by learning temporal patterns from data. Echo State Networks (ESNs), which are a class of Reservoir Computing, can accurately predict the chaotic dynamics well beyond the…

This paper proposes a data-driven control framework to regulate an unknown, stochastic linear dynamical system to the solution of a (stochastic) convex optimization problem. Despite the centrality of this problem, most of the available…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that…

We introduce new techniques to the analysis of neural spatiotemporal dynamics via applying $\epsilon$-machine reconstruction to electroencephalography (EEG) microstate sequences. Microstates are short duration quasi-stable states of the…

We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…

Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…

Network scientists often use complex dynamic processes to describe network contagions, but tools for fitting contagion models typically assume simple dynamics. Here, we address this gap by developing a nonparametric method to reconstruct a…