Related papers: Fourier Features for Identifying Differential Equa…

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is a necessary step to draw conclusions from these data, and it often becomes quite essential to construct dynamical models using these…

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…

Recent successes of deep learning-based recognition rely on maintaining the content related to the main-task label. However, how to explicitly dispel the noisy signals for better generalization in a controllable manner remains an open…

Functional connectivity estimates are highly sensitive to analysis choices and can be dominated by noise when the number of sampled time points is small relative to network dimensionality. This issue is particularly acute in fMRI, where…

We present a deep neural network to reduce coherent noise in three-dimensional quantitative phase imaging. Inspired by the cycle generative adversarial network, the denoising network was trained to learn a transform between two image…

Noisy images are a challenge to image compression algorithms due to the inherent difficulty of compressing noise. As noise cannot easily be discerned from image details, such as high-frequency signals, its presence leads to extra bits…

Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing time signals based on non-autonomous dynamical equations.…

Change detection is a widely adopted technique in remote sense imagery (RSI) analysis in the discovery of long-term geomorphic evolution. To highlight the areas of semantic changes, previous effort mostly pays attention to learning…

Testing fairness is a major concern in psychometric and educational research. A typical approach for ensuring testing fairness is through differential item functioning (DIF) analysis. DIF arises when a test item functions differently across…

We revisit the task of releasing marginal queries under differential privacy with additive (correlated) Gaussian noise. We first give a construction for answering arbitrary workloads of weighted marginal queries, over arbitrary domains. Our…

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…

Measurement noise is an integral part while collecting data of a physical process. Thus, noise removal is necessary to draw conclusions from these data, and it often becomes essential to construct dynamical models using these data. We…

Choosing which properties of the data to use as input to multivariate decision algorithms -- a.k.a. feature selection -- is an important step in solving any problem with machine learning. While there is a clear trend towards training…

In this paper we introduce and study a new feature-preserving nonlinear anisotropic diffusion for denoising signals. The proposed partial differential equation is based on a novel diffusivity coefficient that uses a nonlocal automatically…

A new technique for reliably identifying point sources in millimeter/sub-millimeter wavelength maps is presented. This method accounts for the frequency dependence of noise in the Fourier domain as well as non-uniformities in the coverage…

Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…

This paper addresses the problem of consistently estimating a continuous-time (CT) diffusively coupled network (DCN) to identify physical components in a physical network. We develop a three-step frequency-domain identification method for…

Random Fourier features provide a way to tackle large-scale machine learning problems with kernel methods. Their slow Monte Carlo convergence rate has motivated the research of deterministic Fourier features whose approximation error can…

Noise is a significant challenge in imaging. Conventional intensity-based techniques mitigate noise through various filtering methods, but they often require prior knowledge of noise characteristics and struggle, especially under low-light…

I present a family of algorithms to reduce noise in astrophysical im- ages and image sequences, preserving more information from the original data than is retained by conventional techniques. The family uses locally adaptive filters ("noise…