Related papers: Spectral proper orthogonal decomposition
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)…
While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…
This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal…
Superheated steam is widely employed in various energy systems, particularly in power plants, chemical industries, and other applications where high-temperature and high-pressure steam is essential for efficient energy conversion and…
We propose a novel variant of the Localized Orthogonal Decomposition (LOD) method for time-harmonic scattering problems of Helmholtz type with high wavenumber $\kappa$. On a coarse mesh of width $H$, the proposed method identifies local…
The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures…
This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…
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…
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…
High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient…
The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…
In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…
We present a new method for generating robust guesses for unstable periodic orbits (UPOs) by post-processing turbulent data using dynamic mode decomposition (DMD). The approach relies on the identification of near-neutral, repeated…
We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two…
The definition of partial differential equation (PDE) models usually involves a set of parameters whose values may vary over a wide range. The solution of even a single set of parameter values may be quite expensive. In many cases, e.g.,…
This work aims to interpolate parametrized Reduced Order Model (ROM) basis constructed via the Proper Orthogonal Decomposition (POD) to derive a robust ROM of the system's dynamics for an unseen target parameter value. A novel non-intrusive…
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…
Time-delay embedding is an increasingly popular starting point for data-driven reduced-order modeling efforts. In particular, the singular value decomposition (SVD) of a block Hankel matrix formed from successive delay embeddings of the…
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 propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…