Related papers: Machine Learning of Partial Differential Equations…
This paper focuses on a stochastic system identification problem: given time series observations of a stochastic differential equation (SDE) driven by L\'{e}vy $\alpha$-stable noise, estimate the SDE's drift field. For $\alpha$ in the…
Noise is a part of data whether the data is from measurement, experiment or ... A few techniques are suggested for noise reduction to improve the data quality in recent years some of which are based on wavelet, orthogonalization and neural…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…
The changes in brightness of an astronomical source as a function of time are key probes into that source's physics. Periodic and quasi-periodic signals are indicators of fundamental time (and length) scales in the system, while stochastic…
We investigate methods for learning partial differential equation (PDE) models from spatiotemporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select…
We present a new deterministic algorithm for the sparse Fourier transform problem, in which we seek to identify k << N significant Fourier coefficients from a signal of bandwidth N. Previous deterministic algorithms exhibit quadratic…
Despite the large research effort devoted to learning dependencies between time series, the state of the art still faces a major limitation: existing methods learn partial correlations but fail to discriminate across distinct frequency…
We extend the recent sparse Fourier transform algorithm of (Lawlor, Christlieb, and Wang, 2013) to the noisy setting, in which a signal of bandwidth N is given as a superposition of k << N frequencies and additive noise. We present two such…
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…
A signal processing method designed for the detection of linear (coherent) behaviors among random fluctuations is presented. It is dedicated to the study of data recorded from nonlinear physical systems. More precisely the method is suited…
Machine learning based partial differential equations (PDEs) solvers have received great attention in recent years. Most progress in this area has been driven by deep neural networks such as physics-informed neural networks (PINNs) and…
In classical approaches of dynamic network identification, in order to identify a system (module) embedded in a dynamic network, one has to formulate a Multi-input-Single-output (MISO) identification problem that requires identification of…
We have presented a new and alternative algorithm for noise reduction using the methods of discrete wavelet transform and numerical differentiation of the data. In our method the threshold for reducing noise comes out automatically. The…
The difficulty in frequency domain identification is that frequency components of arbitrary inputs and outputs are not related by the system's transfer function if signals are windowed. When rectangular windows are used, it is well known…
Fourier Neural Operators (FNO) offer a principled approach to solving challenging partial differential equations (PDE) such as turbulent flows. At the core of FNO is a spectral layer that leverages a discretization-convergent representation…
In this review, we survey the latest approaches and techniques developed to overcome the spectral bias towards low frequency of deep neural network learning methods in learning multiple-frequency solutions of partial differential equations.…
The growing field of nano nuclear magnetic resonance (nano-NMR) seeks to estimate spectra or discriminate between spectra of minuscule amounts of complex molecules. While this field holds great promise, nano-NMR experiments suffer from…
The modulating functions method has been used for the identification of linear and nonlinear systems. In this paper, we generalize this method to the on-line identification of fractional order systems based on the Riemann-Liouville…
One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…