Related papers: A new approach to proper orthogonal decomposition …

The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques…

This note proves, for simplicity for the heat equation, that using BDF2 as time stepping scheme in POD-ROM methods with snapshots based on difference quotients gives both the optimal second order error bound in time and pointwise estimates.

Proper orthogonal decomposition methods for model reduction utilize information about the solution at certain time and parameter points to generate a reduced space basis. In this paper, we compare two proper orthogonal decomposition methods…

We present a new methodology for decomposing flows with multiple transports that further extends the shifted proper orthogonal decomposition (sPOD). The sPOD tries to approximate transport-dominated flows by a sum of co-moving data fields.…

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…

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…

The spectral proper orthogonal decomposition (SPOD) is a newly introduced extension of snapshot POD that recently gained attention but also brought up controversial issues. Within the first proposition, the approach was mainly presented in…

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

This paper puts forth several closure models for the proper orthogonal decomposition (POD) reduced order modeling of fluid flows. These new closure models, together with other standard closure models, are investigated in the numerical…

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…

The proper orthogonal decomposition (POD) is a powerful classical tool in fluid mechanics used, for instance, for model reduction and extraction of coherent flow features. However, its applicability to high-resolution data, as produced by…

We propose a new hybridizable discontinuous Galerkin (HDG) model order reduction technique based on proper orthogonal decomposition (POD). We consider the heat equation as a test problem and prove error bounds that converge to zero as the…

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…

In this paper we consider the numerical approximation of a semilinear reaction-diffusion model problem (PDEs) by means of reduced order methods (ROMs) based on proper orthogonal decomposition (POD). We focus on the time integration of the…

Modal decomposition methods are important for characterizing the low-dimensional dynamics of complex systems, including turbulent flows. Different methods have varying data requirements and produce modes with different properties. Spectral…

This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…

The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with…

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…

This paper studies discretization of time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Most of the analysis in the literature has been performed on fully-discrete…

We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…