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We consider the problem of reconstructing missing data on a smooth manifold from incomplete and nonuniform samples. While classical methods for manifold approximation typically assume quasi-uniform data, their performance deteriorates…

Numerical Analysis · Mathematics 2026-04-15 David Levin

The use of proper orthogonal decomposition (POD) to explore the complex fluid flows that are common in engineering applications is increasing and has yielded new physical insights. However, for most engineering systems the dimension of the…

Fluid Dynamics · Physics 2009-06-01 Andrew Duggleby , Mark R. Paul

Remotely sensed data are sparse, which means that data have missing values, for instance due to cloud cover. This is problematic for applications and signal processing algorithms that require complete data sets. To address the sparse data…

Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon…

Machine Learning · Computer Science 2025-04-01 Oliver T. Schmidt

This study focuses on the stratification patterns and dynamic evolution of reservoir water temperatures, aiming to estimate and reconstruct the temperature field using limited and noisy local measurement data. Due to complex measurement…

Machine Learning · Computer Science 2025-02-21 Qianyu He , Huaiwei Sun , Yubo Li , Zhiwen You , Qiming Zheng , Yinghan Huang , Sipeng Zhu , Fengyu Wang

We present a method for combining proper orthogonal decomposition (POD) bases optimized with respect to different norms into a single complete basis. We produce a basis combining decompositions optimized with respect to turbulent kinetic…

Fluid Dynamics · Physics 2023-03-30 Peder J. Olesen , Azur Hodžić , Clara M. Velte

In this paper, we combine concepts of the generalized multiscale finite element method and mode decomposition methods to construct a robust local-global approach for model reduction of flows in high-contrast porous media. This is achieved…

Computational Physics · Physics 2013-01-25 Mehdi Ghommem , Michael Presho , Victor M. Calo , Yalchin Efendiev

In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for…

Numerical Analysis · Mathematics 2020-07-24 Xiaoying Dai , Xiong Kuang , Jack Xin , Aihui Zhou

It is expensive to compute residual diffusivity in chaotic in-compressible flows by solving advection-diffusion equation due to the formation of sharp internal layers in the advection dominated regime. Proper orthogonal decomposition (POD)…

Computational Physics · Physics 2019-10-02 Jiancheng Lyu , Jack Xin , Yifeng Yu

In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…

Numerical Analysis · Mathematics 2026-05-26 Gabriele Codega , Anna Ivagnes , Nicola Demo , Gianluigi Rozza

In this paper, we introduce the proper latent decomposition (PLD) as a generalization of the proper orthogonal decomposition (POD) on manifolds. PLD is a nonlinear reduced-order modeling technique for compressing high-dimensional data into…

Machine Learning · Computer Science 2024-12-03 Daniel Kelshaw , Luca Magri

Proper Orthogonal Decomposition (POD) is a widely used technique for the construction of low-dimensional approximation spaces from high-dimensional input data. For large-scale applications and an increasing amount of input data vectors,…

Numerical Analysis · Mathematics 2021-06-09 Christian Himpe , Tobias Leibner , Stephan Rave

We propose a space-time reduced-order model (ROM) for nonlinear dynamical systems, building upon previous work on linear systems. Whereas most ROMs are space-only in that they reduce only the spatial dimension of the state, the proposed…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Aaron Towne

We present a numerical methodology for construction of reduced order models, ROMs, of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition, SPOD, is applied to…

Fluid Dynamics · Physics 2019-07-24 Hugo F. S. Lui , William R. Wolf

We introduce a modal representation for Lagrangian trajectories in turbulence, termed Lagrangian Proper Orthogonal Decomposition (LPOD). An ensemble of particle trajectories is used to construct velocity time series, which are normalized…

Fluid Dynamics · Physics 2026-04-27 Ron Shnapp , Stefano Brizzolara

We propose a novel method for model-based time super-sampling of turbulent flow fields. The key enabler is the identification of an empirical Galerkin model from the projection of the Navier-Stokes equations on a data-tailored basis. The…

We present a formulation of proper orthogonal decomposition (POD) producing a velocity-temperature basis optimized with respect to an $H^1$ dissipation norm. This decomposition is applied, along with a conventional POD optimized with…

Present day computational fluid dynamics simulations generate extremely large amounts of data, sometimes on the order of TB/s. Often, a significant fraction of this data is discarded because current storage systems are unable to keep pace.…

Computational Engineering, Finance, and Science · Computer Science 2021-03-03 Heather Pacella , Alec Dunton , Alireza Doostan , Gianluca Iaccarino

This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique…

Numerical Analysis · Mathematics 2026-05-29 Nicole Aretz , Karen Willcox

In most photoacoustic (PA) measurements, variations in speed-of-sound (SOS) of the subject are neglected under the assumption of acoustic homogeneity. Biological tissue with spatially heterogeneous SOS cannot be accurately reconstructed…