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Sparse Identification of Nonlinear Dynamical Systems (SINDy) is a powerful tool for the data-driven discovery of governing equations. However, it encounters challenges when modeling complex dynamical systems involving high-order derivatives…

We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…

Data-driven methods of model identification are able to discern governing dynamics of a system from data. Such methods are well suited to help us learn about systems with unpredictable evolution or systems with ambiguous governing dynamics…

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…

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…

Signal analysis and classification is fraught with high levels of noise and perturbation. Computer-vision-based deep learning models applied to spectrograms have proven useful in the field of signal classification and detection; however,…

In this work we analyze the effectiveness of the Sparse Identification of Nonlinear Dynamics (SINDy) technique on three benchmark datasets for nonlinear identification, to provide a better understanding of its suitability when tackling real…

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…

Phase retrieval consists in the recovery of an unknown signal from phaseless measurements of its usually complex-valued Fourier transform. Without further assumptions, this problem is notorious to be severe ill posed such that the recovery…

Data-driven discovery of governing equations from noisy observations remains a fundamental challenge in scientific machine learning. While GENERIC formalism informed neural networks (GFINNs) provide a principled framework that enforces the…

To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…

Quantum feature maps offer expressive embeddings for classical learning tasks, and augmenting sparse identification of nonlinear dynamics (SINDy) with such features is a natural but unexplored direction. We introduce \textbf{Q-SINDy}, a…

To reduce the complexity of infrared spectroscopy hardware while maintaining performance, a data informed, task-specific, spectral collection approach termed Sparse Infrared Spectroscopy (SIRS) is developed. Using a numerically based…

The Sparse Identification of Nonlinear Dynamics (SINDy) algorithm can be applied to stochastic differential equations to estimate the drift and the diffusion function using data from a realization of the SDE. The SINDy algorithm requires…

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally…

We propose a supervised learning algorithm for machine learning applications. Contrary to the model developing in the classical methods, which treat training, validation, and test as separate steps, in the presented approach, there is a…

We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso…

Under the frequency domain framework for weakly dependent functional time series, a key element is the spectral density kernel which encapsulates the second-order dynamics of the process. We propose a class of spectral density kernel…

Inference of instrumental variable regression models with many weak instruments attracts many attentions recently. To extend the classical Anderson-Rubin test to high-dimensional setting, many procedures adopt ridge-regularization. However,…

We investigate the sparse functional identification of complex cells and the decoding of visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm of both temporal and spatio-temporal stimuli is formulated as a…