Related papers: Sparse Identification of Nonlinear Duffing Oscilla…

Describing dynamic medical systems using machine learning is a challenging topic with a wide range of applications. In this work, the possibility of modeling the blood glucose level of diabetic patients purely on the basis of measured data…

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

Linear system identification and sparse dictionary learning can both be seen as structured matrix factorization problems. However, these two problems have historically been studied in isolation by the systems theory and machine learning…

Differential equations and numerical methods are extensively used to model various real-world phenomena in science and engineering. With modern developments, we aim to find the underlying differential equation from a single observation of…

This paper leverages recent advances in high derivatives reconstruction from noisy-time series and sparse multivariate polynomial identification in order to improve the process of parsimoniously identifying, from a small amount of data,…

In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…

In many compressive sensing problems today, the relationship between the measurements and the unknowns could be nonlinear. Traditional treatment of such nonlinear relationships have been to approximate the nonlinearity via a linear model…

This paper deals with the error processing problem of sparse identification of nonlinear dynamical systems(SINDy) through introducing the $L_\infty$ approximation to take place of the former $L_2$ approximation. The motivation is that the…

Functional linear discriminant analysis offers a simple yet efficient method for classification, with the possibility of achieving a perfect classification. Several methods are proposed in the literature that mostly address the…

This paper considers the problem of estimating linear dynamic system models when the observations are corrupted by random disturbances with nonstandard distributions. The paper is particularly motivated by applications where sensor…

This paper addresses identification of sparse linear and noise-driven continuous-time state-space systems, i.e., the right-hand sides in the dynamical equations depend only on a subset of the states. The key assumption in this study, is…

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured…

In this paper we propose a new method to detect and classify coexisting solutions in nonlinear systems. We focus on mechanical and structural systems where we usually avoid multistability for safety and reliability. We want to be sure that…

While linear systems have been useful in solving problems across different fields, the need for improved performance and efficiency has prompted them to operate in nonlinear modes. As a result, nonlinear models are now essential for the…

Networks of nonlinear oscillators can exhibit complex collective behaviour ranging from synchronised states to chaos. Here, we simulate the dynamics of three coupled Duffing oscillators whose multiple equilibrium states can be used for…

Regularized methods have been widely applied to system identification problems without known model structures. This paper proposes an infinite-dimensional sparse learning algorithm based on atomic norm regularization. Atomic norm…

The oscillatory response of nonlinear systems exhibits characteristic phenomena such as multistability, discontinuous jumps and hysteresis. These can be utilized in applications leading, e.g., to precise frequency measurement, mixing,…

We investigate the impact of nonlinear damping on the dynamics of a nanomechanical doubly clamped beam. The beam is driven into nonlinear regime and the response is measured by a displacement detector. For data analysis we introduce a…

Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For…

Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear…