Related papers: Gappy spectral proper orthogonal decomposition
In many real-world scenarios, obtaining fully observed samples is prohibitively expensive or even infeasible, while partial and noisy observations are comparatively easy to collect. In this work, we study distribution restoration with…
Proper orthogonal decomposition (POD) is often employed in developing reduced-order models (ROM) in fluid flows for design, control, and optimization. Contrary to the usual practice where velocity field is the focus, we apply the POD…
Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable. It is popular as it comes with theoretical guarantees on…
We present the Super-Localized Orthogonal Decomposition (SLOD) method for the numerical homogenization of linear elasticity problems with multiscale microstructures modeled by a heterogeneous coefficient field without any periodicity or…
Remote sensing data provide a low-cost solution for large-scale monitoring of air pollution via the retrieval of aerosol optical depth (AOD), but is often limited by cloud contamination. Existing methods for AOD reconstruction rely on…
The object of this work is to design an adequate regularization for the problem of recovering missing Fourier coefficients, particularly in some non standard situations were low frequency coefficients are lost. In the framework of non-local…
The GRAPPA (GeneRalized Autocalibrating Partially Parallel Acquisitions) method of parallel MRI makes use of an autocalibration scan (ACS) to determine a set of synthesis coefficients to be used in the image reconstruction. For EPI time…
Highly accurate geometric precision and dense image features characterize True Digital Orthophoto Maps (TDOMs), which are in great demand for applications such as urban planning, infrastructure management, and environmental monitoring.…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…
Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed…
This paper introduces the approach of Randomized Orthogonal Decomposition (ROD) for producing twin data models in order to overcome the drawbacks of existing reduced order modelling techniques. When compared to Fourier empirical…
We develop a numerical method to reconstruct systems of ordinary differential equations (ODEs) from time series data without {\it a priori} knowledge of the underlying ODEs using sparse basis learning and sparse function reconstruction. We…
We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the…
We introduce a novel algorithm, $\textit{COD}$ -- Compact Opacity Distribution, for shape reconstruction of a celestial body that has been observed to occult a star, using the photometric time-series observations of the occultation.…
Motivated by the aero-acoustic feedback loop phenomenon in high speed free jets and impinging jets, a thorough examination of a POD (Proper Orthogonal Decomposition)-Galerkin method to determine the average convection velocity of coherent…
Integral field spectroscopy can map astronomical objects spatially and spectroscopically. Due to instrumental and atmospheric effects, it is common for integral field instruments to yield a sampling of the sky image that is both irregular…
This paper concerns the data-driven sensor deployment problem in large spatiotemporal fields. Traditionally, sensor deployment strategies have been heavily dependent on model-based planning approaches. However, model-based approaches do not…
Distortion rectification is often required for fisheye images. The generation-based method is one mainstream solution due to its label-free property, but its naive skip-connection and overburdened decoder will cause blur and incomplete…
We develop a distribution-free, unsupervised anomaly detection method called ECAD, which wraps around any regression algorithm and sequentially detects anomalies. Rooted in conformal prediction, ECAD does not require data exchangeability…
The orthogonal matching pursuit (OMP) is one of the mainstream algorithms for sparse data reconstruction or approximation. It acts as a driving force for the development of several other greedy methods for sparse data reconstruction, and it…