Related papers: Fourier Weak SINDy: Spectral Test Function Selecti…
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 success of the compressed sensing paradigm has shown that a substantial reduction in sampling and storage complexity can be achieved in certain linear and non-adaptive estimation problems. It is therefore an advisable strategy for…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
Noisy supervision refers to supervising image restoration learning with noisy targets. It can alleviate the data collection burden and enhance the practical applicability of deep learning techniques. However, existing methods suffer from…
The sparse identification of nonlinear dynamics (SINDy) approach can discover the governing equations of dynamical systems based on measurement data, where the dynamical model is identified as the sparse linear combination of the given…
The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…
The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE…
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…
This paper proposes a sparse identification of nonlinear dynamics (SINDy) with control and exogenous inputs for highly accurate and reliable prediction. Although SINDy is recognized as a remarkable approach for identifying nonlinear…
In many applications, training machine learning models involves using large amounts of human-annotated data. Obtaining precise labels for the data is expensive. Instead, training with weak supervision provides a low-cost alternative. We…
We introduce an equation learning framework to identify a closed set of equations for moment quantities in 1D thermal radiation transport (TRT) in optically thin media. While optically thick media admits a well-known diffusive closure, the…
This paper presents a novel approach for estimating the modes of an observed non-stationary mixture signal. A link is first established between the short-time Fourier transform and the sparse sampling theory, where the observations are…
This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…
We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are closely related, yet there is limited work in exploring this…
Spectral characterization of noise environments that lead to the decoherence of qubits is critical to developing robust quantum technologies. While dynamical decoupling offers one of the most successful approaches to characterize noise…
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…
This paper addresses the problem of expressing a signal as a sum of frequency components (sinusoids) wherein each sinusoid may exhibit abrupt changes in its amplitude and/or phase. The Fourier transform of a narrow-band signal, with a…
Identifying the governing equations of a dynamical system is one of the most important tasks for scientific modeling. However, this procedure often requires high-quality spatio-temporal data uniformly sampled on structured grids. In this…
The Weak form Estimation of Nonlinear Dynamics (WENDy) method is a recently proposed class of parameter estimation algorithms that exhibits notable noise robustness and computational efficiency. This work examines the coverage and bias…
Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations…