Related papers: Reconstruction, forecasting, and stability of chao…

This paper analyzes the stability-related properties of Long Short-Term Memory (LSTM) networks and investigates their use as the model of the plant in the design of Model Predictive Controllers (MPC). First, sufficient conditions…

Current methods for time series forecasting struggle in the online scenario, since it is difficult to preserve long-term dependency while adapting short-term changes when data are arriving sequentially. Although some recent methods solve…

Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…

Identification of the unknown parameters and orders of fractional chaotic systems is of vital significance in controlling and synchronization of fractional-order chaotic systems. However there exist basic hypotheses in traditional…

Chimeras and branching are two archetypical complex phenomena that appear in many physical systems; because of their different intrinsic dynamics, they delineate opposite non-trivial limits in the complexity of wave motion and present…

Deep learning has achieved strong performance in Time Series Forecasting (TSF). However, we identify a critical representation paradox, termed Latent Chaos: models with accurate predictions often learn latent representations that are…

The Extended Long Short-Term Memory (xLSTM) network has demonstrated strong capability in modeling complex long-term dependencies in time series data. Despite its success, the deterministic architecture of xLSTM limits its representational…

We introduce "state space persistence analysis" for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent…

This article presents a general framework for recovering missing dynamical systems using available data and machine learning techniques. The proposed framework reformulates the prediction problem as a supervised learning problem to…

This chapter offers a principled approach to the prediction of chaotic systems from data. First, we introduce some concepts from dynamical systems' theory and chaos theory. Second, we introduce machine learning approaches for…

Short-term traffic forecasting based on deep learning methods, especially recurrent neural networks (RNN), has received much attention in recent years. However, the potential of RNN-based models in traffic forecasting has not yet been fully…

Hidden semi-Markov models (HSMMs) are latent variable models which allow latent state persistence and can be viewed as a generalization of the popular hidden Markov models (HMMs). In this paper, we introduce a novel spectral algorithm to…

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.…

Recurrent neural networks, and in particular long short-term memory (LSTM) networks, are a remarkably effective tool for sequence modeling that learn a dense black-box hidden representation of their sequential input. Researchers interested…

The capabilities of recurrent neural networks and Koopman-based frameworks are assessed in the prediction of temporal dynamics of the low-order model of near-wall turbulence by Moehlis et al. (New J. Phys. 6, 56, 2004). Our results show…

In the context of filtering chaotic dynamical systems it is well-known that partial observations, if sufficiently informative, can be used to control the inherent uncertainty due to chaos. The purpose of this paper is to investigate, both…

This work proposes a structure-preserving model reduction method for marginally stable linear time-invariant (LTI) systems. In contrast to Lyapunov-stability-based approaches---which ensure the poles of the reduced system remain in the open…

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…

Many modern datasets don't fit neatly into $n \times p$ matrices, but most techniques for measuring statistical stability expect rectangular data. We study methods for stability assessment on non-rectangular data, using statistical learning…

Simulations of chaotic systems can only produce high-fidelity trajectories if the initial and boundary conditions are well specified. When these conditions are unknown but measurements are available, variational state estimation can…