Related papers: Dynamically learning the parameters of a chaotic s…
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…
Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…
Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method utilizes deep neural networks (DNNs) to construct a model for…
We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…
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…
Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…
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.…
Low-dimensional chaotic systems such as the Lorenz-63 model are commonly used to benchmark system-agnostic methods for learning dynamics from data. Here we show that learning from noise-free observations in such systems can be achieved up…
The identification of the governing equations of chaotic dynamical systems from data has recently emerged as a hot topic. While the seminal work by Brunton et al. reported proof-of-concepts for idealized observation setting for…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Complex and nonlinear dynamical systems often involve parameters that change with time, accurate tracking of which is essential to tasks such as state estimation, prediction, and control. Existing machine-learning methods require full state…
Despite rapid progress in live-imaging techniques, many complex biophysical and biochemical systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an…
Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime. The challenge is even greater when the physics underlying such systems is…
We introduce a simple method to estimate the system parameters in continuous dynamical systems from the time series. In this method, we construct a modified system by introducing some constants (controlling constants) into the given…
This paper describes how to determine the parameter values of the chaotic Lorenz system from one of its variables waveform. The geometrical properties of the system are used firstly to reduce the parameter search space. Then, a…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…
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…
The problem of dynamic estimation of all parameters of a model representing chaotic and hyperchaotic systems using information from a scalar measured output is solved. The variational calculus based method is robust in the presence of…
We consider the problem of learning the parameters of a $N$-dimensional stochastic linear dynamics under both full and partial observations from a single trajectory of time $T$. We introduce and analyze a new estimator that achieves a small…