Related papers: On the Convergence of the SINDy Algorithm

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…

With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…

In order to extract governing equations from time-series data, various approaches are proposed. Among those, sparse identification of nonlinear dynamics (SINDy) stands out as a successful method capable of modeling governing equations with…

In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define…

The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…

We investigate implicit regularization schemes for gradient descent methods applied to unpenalized least squares regression to solve the problem of reconstructing a sparse signal from an underdetermined system of linear measurements under…

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…

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…

In this work, we revisit dictionary-based sparse regression, in particular, Sequential Threshold Least Squares (STLS), and propose a score-guided library selection to provide practical guidance for data-driven modeling, with emphasis on…

Modern societies have an abundance of data yet good system models are rare. Unfortunately, many of the current system identification and machine learning techniques fail to generalize outside of the training set, producing models that…

The sparse identification of nonlinear dynamical systems (SINDy) is a data-driven technique employed for uncovering and representing the fundamental dynamics of intricate systems based on observational data. However, a primary obstacle in…

The SINDy algorithm has been successfully used to identify the governing equations of dynamical systems from time series data. However, SINDy assumes the user has prior knowledge of the variables in the system and of a function library that…

A general framework for recovering drift and diffusion dynamics from sampled trajectories is presented for the first time for stochastic delay differential equations. The core relies on the well-established SINDy algorithm for the sparse…

Sparse Identification of Nonlinear Dynamics (SINDy) has been shown to successfully recover governing equations from data; however, this approach assumes the initial condition to be exactly known in advance and is sensitive to noise. In this…

We present a new algorithm and the corresponding convergence analysis for the regularization of linear inverse problems with sparsity constraints, applied to a new generalized sparsity promoting functional. The algorithm is based on the…

Sparse regression has emerged as a popular technique for learning dynamical systems from temporal data, beginning with the SINDy (Sparse Identification of Nonlinear Dynamics) framework proposed by arXiv:1509.03580. Quantifying the…

Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…

This paper treats the problem of minimizing a general continuously differentiable function subject to sparsity constraints. We present and analyze several different optimality criteria which are based on the notions of stationarity and…

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,…

System identification plays a crucial role in physics and machine learning for discovering governing equations directly from data. A powerful approach is the Sparse Identification of Nonlinear Dynamics (SINDy) method, which assumes that…