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Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…

Mathematical Physics · Physics 2012-07-05 Antti Lipponen , Aku Seppänen , Jari Kaipio

We investigate numerically the 3-D flow around a squareback Ahmed body at Reynolds number Re = 104. Proper Orthogonal Decomposition (POD) is applied to a symmetry-augmented database in order to describe and model the flow dynamics.…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2026-03-31 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

Numerical Analysis · Mathematics 2021-10-18 Zhongjian Wang , Wenlong Zhang , Zhiwen Zhang

Superfluid turbulent wakes behind a square prism are studied theoretically and numerically by proper orthogonal decomposition (POD). POD is a data science approach that can efficiently extract the principal vibration modes of a physical…

Quantum Gases · Physics 2025-06-16 Sota Yoneda , Hiromitsu Takeuchi

We develop a convolutional regularized least squares ($\texttt{CRLS}$) framework for reduced-order modeling of transonic flows with shocks. Conventional proper orthogonal decomposition (POD) based reduced models are attractive because of…

Fluid Dynamics · Physics 2025-11-27 Muhammad Bilal , Ashwin Renganathan

Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…

Fluid Dynamics · Physics 2019-02-25 Jörn Sesterhenn , Amir Shahirpour

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

Numerical Analysis · Mathematics 2024-01-17 Francesco Andreuzzi , Nicola Demo , Gianluigi Rozza

Data-driven decompositions are becoming essential tools in fluid dynamics, allowing for tracking the evolution of coherent patterns in large datasets, and for constructing low order models of complex phenomena. In this work, we analyze the…

Fluid Dynamics · Physics 2020-04-15 M. A. Mendez , M. Balabane , J. -M. Buchlin

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, a stabilized proper orthogonal decomposition (POD) reduced-order model (ROM) is presented for the barotropic vorticity equation. We apply the POD-ROM model to mid-latitude simplified oceanic basins, which are standard…

Fluid Dynamics · Physics 2018-01-29 Omer San , Traian Iliescu

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…

The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…

Numerical Analysis · Mathematics 2024-12-20 Steffen Kastian , Dieter Moser , Stefanie Reese , Lars Grasedyck

Model Order Reduction (MOR) based on Proper Orthogonal Decomposition (POD) and Smooth Particle Hydrodynamics (SPH) has proven effective in various applications. Most MOR methods utilizing POD are implemented within a pure Eulerian…

Computational Physics · Physics 2025-08-04 Lidong Fang , Zilong Song , Kirk Fraser , Huaxiong Huang

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

Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Cong Lin , Oliver Schmidt , Aaron Towne

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2024-12-30 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to…

Fluid Dynamics · Physics 2024-02-20 Diego C. P. Blanco , Eduardo Martini , Kenzo Sasaki , André V. G. Cavalieri

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 work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…

Numerical Analysis · Mathematics 2024-01-22 Maria Strazzullo , Fabio Vicini