相关论文: Discovery of Nonlinear Dynamics with Automated Bas…

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…

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…

Microgrids (MGs) play a crucial role in utilizing distributed energy resources (DERs) like solar and wind power, enhancing the sustainability and flexibility of modern power systems. However, the inherent variability in MG topology, power…

Inferring physical laws from data is a central challenge in science and engineering, including but not limited to healthcare, physical sciences, biosciences, social sciences, sustainability, climate, and robotics. Deep networks offer…

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…

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…

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

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…

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…

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…

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…

Identifying network dynamics is a critical yet challenging task to to understand the mechanism of real-world social systems. There are two types of algorithms, and one requires the knowledge of self-dynamics function, interactive function,…

Hybrid modelling enhances the accuracy and predictive capability of dynamic models by integrating first principles with data-driven methods, effectively mitigating epistemic uncertainties inherent in mechanistic approaches. However, hybrid…

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…

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…

In scientific machine learning, the task of identifying partial differential equations accurately from sparse and noisy data poses a significant challenge. Current sparse regression methods may identify inaccurate equations on sparse and…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

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…

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…

Our ability to predict, control, and ultimately understand complex systems rests on discovering the equations that govern their dynamics. Identifying these equations directly from noisy, limited observations has therefore become a central…