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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…
Identifying nonlinear dynamics and characterizing noise from data is critical across science and engineering for understanding and modeling the behavior of the systems accurately. The modified sparse identification of nonlinear dynamics…
In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…
In differential equation discovery algorithms, numerical differentiation is usually a fixed preliminary step. Current methods improve robustness with data subsampling and sparsity but often ignore the variability from the differentiation…
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…
Forced oscillations may jeopardize the secure operation of power systems. To mitigate forced oscillations, locating the sources is critical. In this paper, leveraging on Sparse Identification of Nonlinear Dynamics (SINDy), an online purely…
Decision formation in perceptual decision-making involves sensory evidence accumulation instantiated by the temporal integration of an internal decision variable towards some decision criterion or threshold, as described by sequential…
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…
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…
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…
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…
Delay Differential Equations (DDEs) are a class of differential equations that can model diverse scientific phenomena. However, identifying the parameters, especially the time delay, that make a DDE's predictions match experimental results…
The quantitative formulation of evolution equations is the backbone for prediction, control, and understanding of dynamical systems across diverse scientific fields. Besides deriving differential equations for dynamical systems based on…
This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…
This paper presents a comprehensive approach to nonlinear dynamics identification for UAVs using a combination of data-driven techniques and theoretical modeling. Two key methodologies are explored: Proportional-Derivative (PD)…
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…
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…
We present a weak formulation and discretization of the system discovery problem from noisy measurement data. This method of learning differential equations from data fits into a new class of algorithms that replace pointwise derivative…
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…