Related papers: Weak SINDy: Galerkin-Based Data-Driven Model Selec…

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…

Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…

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…

The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. It is a natural extension of the classic conforming finite element method for discontinuous…

Data-driven discovery of governing equations from data remains a fundamental challenge in nonlinear dynamics. Although sparse regression techniques have advanced system identification, they struggle with rational functions and noise…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

In many real-world datasets, like WebVision, the performance of DNN based classifier is often limited by the noisy labeled data. To tackle this problem, some image related side information, such as captions and tags, often reveal underlying…

We demonstrate a deep learning framework capable of recovering physical parameters from the Nonlinear Schrodinger Equation (NLSE) under severe noise conditions. By integrating Physics-Informed Neural Networks (PINNs) with automatic…

Real-world multivariate time series, particularly in critical infrastructure such as electrical power grids, are often corrupted by noise and anomalies that degrade the performance of downstream tasks. Standard data cleaning approaches…

Label noise significantly degrades the generalization ability of deep models in applications. Effective strategies and approaches, \textit{e.g.} re-weighting, or loss correction, are designed to alleviate the negative impact of label noise…

System identification is of special interest in science and engineering. This article is concerned with a system identification problem arising in stochastic dynamic systems, where the aim is to estimate the parameters of a system along…

Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse…

A key task in the field of modeling and analyzing nonlinear dynamical systems is the recovery of unknown governing equations from measurement data only. There is a wide range of application areas for this important instance of system…

Trace-wise noise is a type of noise often seen in seismic data, which is characterized by vertical coherency and horizontal incoherency. Using self-supervised deep learning to attenuate this type of noise, the conventional blind-trace deep…

Weakly-Supervised Semantic Segmentation (WSSS) segments objects without a heavy burden of dense annotation. While as a price, generated pseudo-masks exist obvious noisy pixels, which result in sub-optimal segmentation models trained over…

Global optimization of black-box functions from noisy samples is a fundamental challenge in machine learning and scientific computing. Traditional methods such as Bayesian Optimization often converge to local minima on multi-modal…

The estimation of equations from data is of interest in physics. One of the famous methods is the sparse identification of nonlinear dynamics (SINDy), which utilizes sparse estimation techniques to estimate equations from data. Recently, a…

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…

The paper deals with the problem of finding sparse solutions to systems of polynomial equations possibly perturbed by noise. In particular, we show how these solutions can be recovered from group-sparse solutions of a derived system of…

Invertible networks have various benefits for image denoising since they are lightweight, information-lossless, and memory-saving during back-propagation. However, applying invertible models to remove noise is challenging because the input…