Related papers: Reconstruction, forecasting, and stability of chao…
Chaotic time series forecasting has been far less understood despite its tremendous potential in theory and real-world applications. Traditional statistical/ML methods are inefficient to capture chaos in nonlinear dynamical systems,…
Natural systems are typically nonlinear and complex, and it is of great interest to be able to reconstruct a system in order to understand its mechanism, which can not only recover nonlinear behaviors but also predict future dynamics. Due…
The aim of this paper is to address two related estimation problems arising in the setup of hidden state linear time invariant (LTI) state space systems when the dimension of the hidden state is unknown. Namely, the estimation of any finite…
A new algorithm is presented for reconstructing stochastic nonlinear dynamical models from noisy time-series data. The approach is analytical; consequently, the resulting algorithm does not require an extensive global search for the model…
Brains process information through the collective dynamics of large neural networks. Collective chaos was suggested to underlie the complex ongoing dynamics observed in cerebral cortical circuits and determine the impact and processing of…
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…
Certain deterministic non-linear systems may show chaotic behaviour. Time series derived from such systems seem stochastic when analyzed with linear techniques. However, uncovering the deterministic structure is important because it allows…
The advanced operation of future electricity distribution systems is likely to require significant observability of the different parameters of interest (e.g., demand, voltages, currents, etc.). Ensuring completeness of data is, therefore,…
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…
Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized…
This work presents a Long Short-Term Memory (LSTM) network for forecasting a monthly electricity demand time series with a one-year horizon. The novelty of this work is the use of pattern representation of the seasonal time series as an…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
The success of recurrent neural networks (RNNs) has been demonstrated in many applications related to turbulence, including flow control, optimization, turbulent features reproduction as well as turbulence prediction and modeling. With this…
This paper develops a general framework for learning interpretable data representation via Long Short-Term Memory (LSTM) recurrent neural networks over hierarchal graph structures. Instead of learning LSTM models over the pre-fixed…
Dynamic modeling of longitudinal networks has been an increasingly important topic in applied research. While longitudinal network data commonly exhibit dramatic changes in its structures, existing methods have largely focused on modeling…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) form a useful tool for modeling dynamical systems. They are particularly useful for representing environments such as road networks and office…
Replicating chaotic characteristics of non-linear dynamics by machine learning (ML) has recently drawn wide attentions. In this work, we propose that a ML model, trained to predict the state one-step-ahead from several latest historic…
Linear Parameter-Varying (LPV) systems with jumps and piecewise differentiable parameters is a class of hybrid LPV systems for which no tailored stability analysis and stabilization conditions have been obtained so far. We fill this gap…
Uncertainty propagation in high-dimensional nonlinear dynamic structural systems is pivotal in state-of-the-art performance-based design and risk assessment, where uncertainties from both excitations and structures, i.e., the aleatoric…
Traffic prediction is necessary not only for management departments to dispatch vehicles but also for drivers to avoid congested roads. Many traffic forecasting methods based on deep learning have been proposed in recent years, and their…