Related papers: Machine-Precision Prediction of Low-Dimensional Ch…

For complex nonlinear systems, it is challenging to design algorithms that are fast, scalable, and give an accurate approximation of the stability region. This paper proposes a sampling-based approach to address these challenges. By…

I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…

We present safe control of partially-observed linear time-varying systems in the presence of unknown and unpredictable process and measurement noise. We introduce a control algorithm that minimizes dynamic regret, i.e., that minimizes the…

In this work, we study the problem of learning partially observed linear dynamical systems from a single sample trajectory. A major practical challenge in the existing system identification methods is the undesirable dependency of their…

Reservoir computers are powerful tools for chaotic time series prediction. They can be trained to approximate phase space flows and can thus both predict future values to a high accuracy, as well as reconstruct the general properties of a…

This paper presents a novel approach to sustain transient chaos in the Lorenz system through the estimation of safety functions using a transformer-based model. Unlike classical methods that rely on iterative computations, the proposed…

In this paper, the performance of three deep learning methods for predicting short-term evolution and for reproducing the long-term statistics of a multi-scale spatio-temporal Lorenz 96 system is examined. The methods are: echo state…

We introduce a data-driven method and shows its skills for spatiotemporal prediction of high-dimensional chaotic dynamics and turbulence. The method is based on a finite-dimensional approximation of the Koopman operator where the…

We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems. The deep hierarchy is encoded into the LSTM by…

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural…

Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…

For a class of idealized chaotic systems (hyperbolic systems) correlations decay exponentially in time. This result is asymptotic and rigorous. The decay rate is related to the Ruelle-Pollicott resonances. Nearly all chaotic model systems,…

Linear dynamical systems are the foundational statistical model upon which control theory is built. Both the celebrated Kalman filter and the linear quadratic regulator require knowledge of the system dynamics to provide analytic…

Two recent papers on prediction of chaotic systems, one on multi-view embedding1 , and the second on prediction in projection2 provide empirical evidence to support particular prediction methods for chaotic systems. Multi-view embedding1 is…

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…

We consider the problem of learning a realization of a partially observed bilinear dynamical system (BLDS) from noisy input-output data. Given a single trajectory of input-output samples, we provide a finite time analysis for learning the…

The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single long system…

Many natural systems exhibit chaotic behaviour such as the weather, hydrology, neuroscience and population dynamics. Although many chaotic systems can be described by relatively simple dynamical equations, characterizing these systems can…

Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has…

The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…