Related papers: Using Machine Learning to Replicate Chaotic Attrac…
Lyapunov exponents describe the asymptotic behavior of the singular values of large products of random matrices. A direct computation of these exponents is however often infeasible. By establishing a link between Lyapunov exponents and an…
We introduce new machine-learning techniques for analyzing chaotic dynamical systems. The primary objectives of the study include the development of a new and simple method for calculating the Lyapunov exponent using only two trajectory…
Reservoir computing is a novel machine learning algorithm that uses a nonlinear dynamical system to efficiently learn complex temporal patterns from data. The objective of this thesis is to investigate the principles of reservoir computing…
Autonomous Dynamic System (DS)-based algorithms hold a pivotal and foundational role in the field of Learning from Demonstration (LfD). Nevertheless, they confront the formidable challenge of striking a delicate balance between achieving…
Reservoir computing has emerged as a powerful framework for time series modelling and forecasting including the prediction of discontinuous transitions. However, the mechanism behind its success is not yet fully understood. This letter…
We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…
We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its…
Machine learning algorithms have opened a breach in the fortress of the prediction of high-dimensional chaotic systems. Their ability to find hidden correlations in data can be exploited to perform model-free forecasting of spatiotemporal…
We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward…
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…
Handling regime shifts and non-stationary time series in deep learning systems presents a significant challenge. In the case of online learning, when new information is introduced, it can disrupt previously stored data and alter the model's…
Many complex phenomena, from weather systems to heartbeat rhythm patterns, are effectively modeled as low-dimensional dynamical systems. Such systems may behave chaotically under certain conditions, and so the ability to detect chaos based…
Lyapunov exponents can be difficult to determine from experimental data. In particular, when using embedding theory to build chaotic attractors in a reconstruction space, extra "spurious" Lyapunov exponents arise that are not Lyapunov…
Photonic reservoir computing is an emergent technology toward beyond-Neumann computing. Although photonic reservoir computing provides superior performance in environments whose characteristics are coincident with the training datasets for…
Making accurate predictions of chaotic time series is a complex challenge. Reservoir computing, a neuromorphic-inspired approach, has emerged as a powerful tool for this task. It exploits the memory and nonlinearity of dynamical systems…
Power systems dominated by renewable energy encounter frequently large, random disturbances, and a critical challenge faced in power-system management is how to anticipate accurately whether the perturbed systems will return to the…
Reservoir computing (RC) is a machine learning algorithm that can learn complex time series from data very rapidly based on the use of high-dimensional dynamical systems, such as random networks of neurons, called "reservoirs." To implement…
This paper investigates the optimal control problem for a class of discrete-time stochastic systems subject to additive and multiplicative noises. A stochastic Lyapunov equation and a stochastic algebra Riccati equation are established for…
We propose a general strategy for feedback control design of complex dynamical systems exploiting the nonlinear mechanisms in a systematic unsupervised manner. These dynamical systems can have a state space of arbitrary dimension with…
In this study, we investigate the effect of reservoir computing training data on the reconstruction of chaotic dynamics. Our findings indicate that a training time series comprising a few periodic orbits of low periods can successfully…