Related papers: Symbolic Regression on Sparse and Noisy Data with …

Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. In this work, we…

We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By…

In the problem of learning mixtures of linear regressions, the goal is to learn a collection of signal vectors from a sequence of (possibly noisy) linear measurements, where each measurement is evaluated on an unknown signal drawn uniformly…

Identification of nonlinear dynamical systems has been popularized by sparse identification of the nonlinear dynamics (SINDy) via the sequentially thresholded least squares (STLS) algorithm. Many extensions SINDy have emerged in the…

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…

Many studies on acoustic radiation forces focus on characterizing the behavior of acoustic fields. However, the dynamic response of objects, particularly those larger than the wavelength, remains underexplored. Here we bridge this gap by…

Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…

Vortex-induced vibrations (VIV) remain a canonical yet complex manifestation of fluid-structure interactions, where coupled nonlinear dynamics govern the motion of bluff bodies. For several years, we have relied on traditional reduced-order…

Data-driven discovery of governing equations has advanced significantly in recent years; however, existing methods often struggle in multiscale systems where dynamically significant terms may have small coefficients. Therefore, we propose…

Recent progress in autoencoder-based sparse identification of nonlinear dynamics (SINDy) under $\ell_1$ constraints allows joint discoveries of governing equations and latent coordinate systems from spatio-temporal data, including simulated…

Understanding how systems evolve over time often requires discovering the differential equations that govern their behavior. Automatically learning these equations from experimental data is challenging when the data are noisy or limited,…

The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given…

Sparse system identification of nonlinear dynamic systems is still challenging, especially for stiff and high-order differential equations for noisy measurement data. The use of highly correlated functions makes distinguishing between true…

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…

We formulate sparse support recovery as a salient set identification problem and use information-theoretic analyses to characterize the recovery performance and sample complexity. We consider a very general model where we are not restricted…

Inferring the structure and dynamics of network models is critical to understanding the functionality and control of complex systems, such as metabolic and regulatory biological networks. The increasing quality and quantity of experimental…

Automated scientific discovery aims to improve scientific understanding through machine learning. A central approach in this field is symbolic regression, which uses genetic programming or sparse regression to learn interpretable…

Identifying dynamical systems characterized by nonlinear parameters presents significant challenges in deriving mathematical models that enhance understanding of physics. Traditional methods, such as Sparse Identification of Nonlinear…

Sparse Identification of Nonlinear Dynamics (SINDy) is a powerful method for discovering parsimonious governing equations from data, but it often requires expert tuning of candidate libraries. We propose an LLM-aided SINDy pipeline that…

Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpretable, in the sense of being sparse or parsimonious. Sparse…