Related papers: Physics-Informed Echo State Networks for Chaotic S…

At the heart of time-series forecasting (TSF) lies a fundamental challenge: how can models efficiently and effectively capture long-range temporal dependencies across ever-growing sequences? While deep learning has brought notable progress,…

Echo State Networks (ESNs) are a class of single-layer recurrent neural networks with randomly generated internal weights, and a single layer of tuneable outer weights, which are usually trained by regularised linear least squares…

Echo State Networks (ESNs) are typically presented as efficient, readout-trained recurrent models, yet their dynamics and design are often guided by heuristics rather than first principles. We recast ESNs explicitly as state-space models…

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have…

The Echo State Network (ESN) is a class of Recurrent Neural Network with a large number of hidden-hidden weights (in the so-called reservoir). Canonical ESN and its variations have recently received significant attention due to their…

Many researchers are interested to use Extended Kalman Filter (EKF) for state estimation of complex nonlinear dynamics with uncertainties which modeled with white noises. On the other hand behavior of the chaotic systems in time domain…

Due to the increasing system stability issues caused by the technological revolutions of power system equipment, the assessment of the dynamic security of the systems for changing operating conditions (OCs) is nowadays crucial. To address…

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…

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.…

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 paper introduces for the first time, to our knowledge, a framework for physics-informed neural networks in power system applications. Exploiting the underlying physical laws governing power systems, and inspired by recent developments…

We present the Physics-Informed Long Short-Term Memory (PI-LSTM) network to reconstruct and predict the evolution of unmeasured variables in a chaotic system. The training is constrained by a regularization term, which penalizes solutions…

Echo State Networks (ESNs) are a class of single layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces…

Partial differential equations, and their chaotic solutions, are pervasive in the modelling of complex systems in engineering, science, and beyond. Data-driven methods can find solutions to partial differential equations with a…

In this work we propose an extension of physics informed supervised learning strategies to parametric partial differential equations. Indeed, even if the latter are indisputably useful in many applications, they can be computationally…

State estimation is the cornerstone of the power system control center since it provides the operating condition of the system in consecutive time intervals. This work investigates the application of physics-informed neural networks (PINNs)…

The data-driven learning of solutions of partial differential equations can be based on a divide-and-conquer strategy. First, the high dimensional data is compressed to a latent space with an autoencoder; and, second, the temporal dynamics…

Echo state networks (ESNs) are a powerful form of reservoir computing that only require training of linear output weights whilst the internal reservoir is formed of fixed randomly connected neurons. With a correctly scaled connectivity…

Drawing on ergodic theory, we introduce a novel training method for machine learning based forecasting methods for chaotic dynamical systems. The training enforces dynamical invariants--such as the Lyapunov exponent spectrum and fractal…

The rapid growth of research in exploiting machine learning to predict chaotic systems has revived a recent interest in Hamiltonian Neural Networks (HNNs) with physical constraints defined by the Hamilton's equations of motion, which…