Related papers: POD reduced order modeling for evolution equations…

Projection-based model reduction is among the most widely adopted methods for constructing parametric Reduced-Order Models (ROM). Utilizing the snapshot data from solving full-order governing equations, the Proper Orthogonal Decomposition…

Snapshot matrices of hyperbolic equations have a slow singular value decay, resulting in inefficient reduced-order models. We develop on the idea of inducing a faster singular value decay by computing snapshots on a transformed spatial…

In this paper, we propose an a-priori error estimate for the model order reduction (MOR) method of space-time proper orthogonal decomposition (space-time POD). The original space-time POD approach extends standard POD by reducing not only…

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

Density-based topology optimization has become a powerful method for automatically generating optimized designs in a wide variety of applications. However, it comes with a large computational cost when solving the physical model requires…

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…

We developed a reduced order model (ROM) using the proper orthogonal decomposition (POD) to compute efficiently the labyrinth and spot like patterns of the FitzHugh-Nagumo (FNH) equation. The FHN equation is discretized in space by the…

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy…

Deterministic solutions to the Sn transport equation can be computationally expensive to calculate. Reduced Order Models (ROMs) provide an efficient means of approximating the Full Order Model (FOM) solution. We propose a novel approach for…

We are interested in the numerical solution of coupled nonlinear partial differential equations (PDEs) in two and three dimensions. Under certain assumptions on the domain, we take advantage of the Kronecker structure arising in standard…

A parametric model order reduction (MOR) approach for simulating the high dimensional models arising in financial risk analysis is proposed on the basis of the proper orthogonal decomposition (POD) approach to generate small model…

Traditional linear approximation methods, such as proper orthogonal decomposition and the reduced basis method, are ill-suited for transport-dominated problems due to the slow decay of the Kolmogorov $n$-width, leading to inefficient and…

In this work, a novel method with an adaptive functional basis for reduced order models (ROM) based on proper orthogonal decomposition (POD) is introduced. The method is intended to be applied in particular to hydrocarbon reservoir…

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…

Snapshot matrices built from solutions to hyperbolic partial differential equations exhibit slow decay in singular values, whereas fast decay is crucial for the success of projection- based model reduction methods. To overcome this problem,…

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a…