Related papers: Sparse Identification of Nonlinear Duffing Oscilla…

Discovering governing equations of complex dynamical systems directly from data is a central problem in scientific machine learning. In recent years, the sparse identification of nonlinear dynamics (SINDy) framework, powered by heuristic…

The Derivative-free nonlinear Kalman Filter is proposed for state estimation and fault diagnosis in distributed parameter systems and particularly in dynamical systems described by partial differential equations of the nonlinear wave type.…

The methodology discussed in this paper aims to enhance choice models' comprehensiveness and explanatory power for forecasting choice outcomes. To achieve these, we have developed a data-driven method that leverages machine learning…

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…

Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…

Ordinary Differential Equations are widespread tools to model chemical, physical, biological process but they usually rely on parameters which are of critical importance in terms of dynamic and need to be estimated directly from the data.…

Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…

We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…

We introduce a new algorithm, called adaptive sparse backfitting algorithm, for solving high dimensional Sparse Additive Model (SpAM) utilizing symmetric, non-negative definite smoothers. Unlike the previous sparse backfitting algorithm,…

Linearising the dynamics of nonlinear mechanical systems is an important and open research area. A common approach is feedback linearisation, which is a nonlinear control method that transforms the input-output response of a nonlinear…

We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field part. An uncertainty quantification is performed by changing…

The problem of estimating a sparse signal from low dimensional noisy observations arises in many applications, including super resolution, signal deconvolution, and radar imaging. In this paper, we consider a sparse signal model with…

The goal of this article is twofold. Firstly, nonlinear system identification is introduced to a wide audience, guiding practicing engineers and newcomers in the field to a sound solution of their data driven modeling problems for nonlinear…

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,…

We present a novel sparse modeling approach to non-rigid shape matching using only the ability to detect repeatable regions. As the input to our algorithm, we are given only two sets of regions in two shapes; no descriptors are provided so…

This paper presents Sparse Partitioning, a Bayesian method for identifying predictors that either individually or in combination with others affect a response variable. The method is designed for regression problems involving binary or…

This article presents an approach for modelling hysteresis in piezoelectric materials, that leverages recent advancements in machine learning, particularly in sparse-regression techniques. While sparse regression has previously been used to…

Nonlinear state-space identification for dynamical systems is most often performed by minimizing the simulation error to reduce the effect of model errors. This optimization problem becomes computationally expensive for large datasets.…

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics…