Related papers: PySINDy: A comprehensive Python package for robust…

We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linear combination of a few linear and nonlinear differential…

Identification of the particle interaction potential is a challenging and important task in dusty plasma, colloids, and smart materials as it allows the characterization of structure formation and helps predict phase transitions. With the…

SHallow REcurrent Decoders (SHRED) provide a deep learning strategy for modeling high-dimensional dynamical systems and/or spatiotemporal data from dynamical system snapshot observations. PySHRED is a Python package that implements SHRED…

The discovery of partial differential equations (PDEs) from experimental data holds great promise for uncovering predictive models of complex physical systems. In this study, we introduce an efficient automatic model discovery framework,…

The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In this…

The explicit governing equation is one of the simplest and most intuitive forms for characterizing physical laws. However, directly discovering partial differential equations (PDEs) from data poses significant challenges, primarily in…

Data normalisation, a common and often necessary preprocessing step in engineering and scientific applications, can severely distort the discovery of governing equations by magnitudebased sparse regression methods. This issue is…

We present a novel extension of the SINDy framework to delay differential equations with {\it distributed delays} and {\it renewal equations}, where typically the dependence from the past manifests via integrals in which the history is…

We extend the data-driven method of Sparse Identification of Nonlinear Dynamics (SINDy) developed by Brunton et al, Proc. Natl. Acad. Sci USA 113 (2016) to the case of delay differential equations (DDEs). This is achieved in a bilevel…

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…

This work designs a scalable, parameter-aware sparse regression framework for discovering interpretable partial differential equations and subgrid-scale closures from multi-parameter simulation data. Building on SINDy (Sparse Identification…

Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

Rheology plays a pivotal role in understanding the flow behavior of fluids by discovering governing equations that relate deformation and stress, known as constitutive equations. Despite the importance of these equations, current methods…

Sparse identification of nonlinear dynamical systems is a topic of continuously increasing significance in the dynamical systems community. Here we explore it at the level of lattice nonlinear dynamical systems of many degrees of freedom.…

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…

Air pollution, particularly particulate matter (PM2.5), poses significant risks to public health and the environment, necessitating accurate prediction and continuous monitoring for effective air quality management. However, air quality…

In recent years there has been a push to discover the governing equations dynamical systems directly from measurements of the state, often motivated by systems that are too complex to directly model. Although there has been substantial work…

Poincar\'e maps are an integral aspect to our understanding and analysis of nonlinear dynamical systems. Despite this fact, the construction of these maps remains elusive and is primarily left to simple motivating examples. In this…