English
Related papers

Related papers: Proper Latent Decomposition

200 papers

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

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…

Computational Physics · Physics 2021-02-03 Elizabeth H. Krath , Forrest L. Carpenter , Paul G. A. Cizmas , David A. Johnston

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 new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…

Numerical Analysis · Mathematics 2018-03-06 Philipp Schulze , Julius Reiss , Volker Mehrmann

In this paper we propose a Local Orthogonal Decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet- and Neumann boundary conditions. For this purpose, we present new boundary correctors which…

Numerical Analysis · Mathematics 2014-07-18 Patrick Henning , Axel Målqvist

We apply the proper orthogonal decomposition (POD) to the nonlinear Schr\"odinger (NLS) equation to derive a reduced order model. The NLS equation is discretized in space by finite differences and is solved in time by structure preserving…

Numerical Analysis · Mathematics 2015-11-26 Bülent Karasözen , Canan Akkoyunlu , Murat Uzunca

In this paper, we propose and analyze a multiscale method for a class of quasilinear elliptic problems of nonmonotone type with spatially multiscale coefficient. The numerical approach is inspired by the Localized Orthogonal Decomposition…

Numerical Analysis · Mathematics 2025-07-28 Maher Khrais , Barbara Verfürth

Spatial network models are used as a simplified discrete representation in a wide range of applications, e.g., flow in blood vessels, elasticity of fiber based materials, and pore network models of porous materials. Nevertheless, the…

Numerical Analysis · Mathematics 2022-10-17 Moritz Hauck , Axel Målqvist

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…

Fluid Dynamics · Physics 2026-05-28 Tomoki Koike , Prakash Mohan , Marc T. Henry de Frahan , Elizabeth Qian , Julie Bessac

This paper focuses on a new framework for reduced order modelling of non-intrusive data with application to 2D flows. To overcome the shortcomings of intrusive model order reduction usually derived by combining the POD and the Galerkin…

Numerical Analysis · Mathematics 2016-11-16 D. A. Bistrian , I. M. Navon

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

Numerical Analysis · Mathematics 2020-11-23 Charumathi V , M. Ramakrishna , Vinita Vasudevan

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

Numerical Analysis · Computer Science 2021-07-07 V. Charumathi , M. Ramakrishna , Vinita Vasudevan

In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation…

Numerical Analysis · Mathematics 2017-03-01 Mario Ohlberger , Barbara Verfürth

Materials synthesis platforms that are designed for autonomous experimentation are capable of collecting multimodal diagnostic data that can be utilized for feedback to optimize material properties. Pulsed laser deposition (PLD) is emerging…

Materials Science · Physics 2024-11-01 Sumner B. Harris , Christopher M. Rouleau , Kai Xiao , Rama K. Vasudevan

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. This work presents the first nonintrusive implementation…

Numerical Analysis · Mathematics 2020-02-05 Vasileios Tsiolakis , Matteo Giacomini , Ruben Sevilla , Carsten Othmer , Antonio Huerta

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computational domains, etc.…

Numerical Analysis · Mathematics 2024-02-06 Zhanhong Ye , Xiang Huang , Hongsheng Liu , Bin Dong

This paper presents "Predictive Pipelined Decoding (PPD)," an approach that speeds up greedy decoding in Large Language Models (LLMs) while maintaining the exact same output as the original decoding. Unlike conventional strategies, PPD…

Computation and Language · Computer Science 2024-07-30 Seongjun Yang , Gibbeum Lee , Jaewoong Cho , Dimitris Papailiopoulos , Kangwook Lee

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

Numerical Analysis · Mathematics 2021-11-03 Stefania Fresca , Andrea Manzoni

In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…

Dynamical Systems · Mathematics 2013-12-17 Dan Yu , Suman Chakravorty

Mapping near-field pollutant concentration is essential to track accidental toxic plume dispersion in urban areas. By solving a large part of the turbulence spectrum, large-eddy simulations (LES) have the potential to accurately represent…

Machine Learning · Statistics 2022-08-03 Bastien X Nony , Mélanie Rochoux , Thomas Jaravel , Didier Lucor