Related papers: Fourier Weak SINDy: Spectral Test Function Selecti…

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…

Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse…

The combination of machine learning (ML) and sparsity-promoting techniques is enabling direct extraction of governing equations from data, revolutionizing computational modeling in diverse fields of science and engineering. The discovered…

Modeling real-world spatio-temporal data is exceptionally difficult due to inherent high dimensionality, measurement noise, partial observations, and often expensive data collection procedures. In this paper, we present Sparse…

Identifying from observation data the governing differential equations of a physical dynamics is a key challenge in machine learning. Although approaches based on SINDy have shown great promise in this area, they still fail to address a…

We develop an efficient and robust high-dimensional sparse Fourier algorithm for noisy samples. Earlier in the paper ``Multi-dimensional sublinear sparse Fourier algorithm" (2016), an efficient sparse Fourier algorithm with $\Theta(ds \log…

This work is concerned with uncertainty quantification in reduced-order dynamical system identification. Reduced-order models for system dynamics are ubiquitous in design and control applications and recent efforts focus on their…

''Noisy'' datasets (regimes with low signal to noise ratios, small sample sizes, faulty data collection, etc) remain a key research frontier for classification methods with both theoretical and practical implications. We introduce FINDER, a…

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using…

In this paper an approach for decreasing the computational effort required for the split-step Fourier method (SSFM) is introduced. It is shown that using the sparsity property of the simulated signals, the compressive sampling algorithm can…

Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…

In this study, a multiple-comparison approach is developed for detecting faint hyperspectral sources. The detection method relies on a sparse and non-negative representation on a highly coherent dictionary to track a spatially varying…

Integrative learning of multiple datasets has the potential to mitigate the challenge of small $n$ and large $p$ that is often encountered in analysis of big biomedical data such as genomics data. Detection of weak yet important signals can…

The data-driven discovery of dynamics via machine learning is currently pushing the frontiers of modeling and control efforts, and it provides a tremendous opportunity to extend the reach of model predictive control. However, many leading…

The interference of fluorescence signals and noise remains a significant challenge in Raman spectrum analysis, often obscuring subtle spectral features that are critical for accurate analysis. Inspired by variational methods similar to…

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…

First principles modeling of physical systems has led to significant technological advances across all branches of science. For nonlinear systems, however, small modeling errors can lead to significant deviations from the true, measured…

In recent years, a number of works have studied methods for computing the Fourier transform in sublinear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is…

In this paper a deterministic sparse Fourier transform algorithm is presented which breaks the quadratic-in-sparsity runtime bottleneck for a large class of periodic functions exhibiting structured frequency support. These functions…

A dedicated algorithm for sparse spectral representation of music sound is presented. The goal is to enable the representation of a piece of music signal, as a linear superposition of as few spectral components as possible. A representation…