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We investigate numerical behaviour of a convection diffusion equation with random coefficients by approximating statistical moments of the solution. Stochastic Galerkin approach, turning the original stochastic problem to a system of…

Numerical Analysis · Mathematics 2021-10-19 Pelin Çiloğlu , Hamdullah Yücel

We propose a projection-based monolithic model order reduction (MOR) procedure for a class of problems in nonlinear mechanics with internal variables. The work is is motivated by applications to thermo-hydro-mechanical (THM) systems for…

Numerical Analysis · Mathematics 2021-09-14 Angelo Iollo , Giulia Sambataro , Tommaso Taddei

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…

Machine Learning · Computer Science 2026-03-04 Hrishikesh Viswanath , Yue Chang , Aleksey Panas , Julius Berner , Peter Yichen Chen , Aniket Bera

We develop a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for the efficient numerical simulation of the parametric Navier-Stokes equations in the stream function-vorticity formulation. Unlike previous…

Numerical Analysis · Mathematics 2022-01-04 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

The second-order Green's function method (GF2) was shown recently to be an accurate self-consistent approach for electronic structure of correlated systems since the self-energy accounts for both the weak and some of the strong correlation.…

Chemical Physics · Physics 2016-03-31 Daniel Neuhauser , Roi Baer , Dominika Zgid

A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…

Numerical Analysis · Mathematics 2021-03-03 Zhu Wang

This paper is concerned with the design of a non-intrusive model order reduction (MOR) for the system of parametric time-domain Maxwell equations. A time- and parameter-independent reduced basis (RB) is constructed by using a two-step…

Numerical Analysis · Mathematics 2021-03-24 Ying Zhao , Liang Li , Kun Li

Reduced-order models of time-dependent partial differential equations (PDEs) where the solution is assumed as a linear combination of prescribed modes are rooted in a well-developed theory. However, more general models where the reduced…

Analysis of PDEs · Mathematics 2021-09-30 William Anderson , Mohammad Farazmand

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…

Systems and Control · Electrical Eng. & Systems 2025-02-04 Behrad Samari , Amy Nejati , Abolfazl Lavaei

In this work, Galerkin projection is used to build Reduced Order Models (ROM) for two-dimensional Rayleigh-B\'enard (RB) convection with no-slip walls. We compare an uncoupled projection approach that uses separate orthonormal bases for…

Fluid Dynamics · Physics 2025-04-07 Enrique Flores-Montoya , André V. G. Cavalieri

Reduced Order Models (ROMs) have gained a great attention by the scientific community in the last years thanks to their capabilities of significantly reducing the computational cost of the numerical simulations, which is a crucial objective…

Numerical Analysis · Mathematics 2024-06-05 Guglielmo Padula , Michele Girfoglio , Gianluigi Rozza

We present a novel certified model order reduction (MOR) algorithm for switched descriptor systems applicable to large-scale systems. Our algorithm combines the idea of [Hossain \& Trenn, Technical report, 2023] to reformulate the switched…

Numerical Analysis · Mathematics 2024-04-17 Mattia Manucci , Benjamin Unger

In this work, we develop a novel numerical scheme to solve the classical Keller--Segel (KS) model which simultaneously preserves its intrinsic mathematical structure and achieves optimal accuracy. The model is reformulated into a gradient…

Numerical Analysis · Mathematics 2025-09-23 X. Yin , X. Lan , Y. Qin

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…

Computational Engineering, Finance, and Science · Computer Science 2024-01-22 Seung Whan Chung , Youngsoo Choi , Pratanu Roy , Thomas Moore , Thomas Roy , Tiras Y. Lin , Du Y. Nguyen , Christopher Hahn , Eric B. Duoss , Sarah E. Baker

In this paper, we bring together the worlds of model order reduction for stochastic linear systems and $\mathcal H_2$-optimal model order reduction for deterministic systems. In particular, we supplement and complete the theory of error…

Numerical Analysis · Mathematics 2020-07-21 Martin Redmann , Melina A. Freitag

Many dynamical systems in the real world are naturally described by latent states with intrinsic orderings, such as "ally", "neutral", and "enemy" relationships in international relations. These latent states manifest through countries'…

Machine Learning · Statistics 2023-02-28 Niklas Stoehr , Benjamin J. Radford , Ryan Cotterell , Aaron Schein

We present multi-adaptive versions of the standard continuous and discontinuous Galerkin methods for ODEs. Taking adaptivity one step further, we allow for individual time-steps, order and quadrature, so that in particular each individual…

Numerical Analysis · Mathematics 2012-05-15 Anders Logg

In order to investigate correspondences between 3D shapes, many methods rely on a feature descriptor which is invariant under almost isometric transformations. An interesting class of models for such descriptors relies on partial…

Numerical Analysis · Mathematics 2019-10-10 Martin Bähr , Michael Breuß , Robert Dachsel

In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional…

Optimization and Control · Mathematics 2020-03-11 Manuel Baumann , Peter Benner , Jan Heiland

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…

Numerical Analysis · Mathematics 2019-08-02 Carmen Gräßle , Michael Hinze , Jens Lang , Sebastian Ullmann