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Model order reduction (MOR) methods that are designed to preserve structural features of a given full order model (FOM) often suffer from a lower accuracy when compared to their non-structure-preserving counterparts. In this paper, we…

Systems and Control · Electrical Eng. & Systems 2022-05-17 Paul Schwerdtner , Matthias Voigt

Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…

Dynamical Systems · Mathematics 2021-10-27 Jonas Kneifl , Julian Hay , Jörg Fehr

Advection-Diffusion-Reaction (ADR) Partial Differential Equations (PDEs) appear in a wide spectrum of applications such as chemical reactors, concentration flows, and biological systems. A large number of these applications require the…

Systems and Control · Electrical Eng. & Systems 2022-03-29 Ahmed Elkhashap , Dirk Abel

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…

Numerical Analysis · Mathematics 2023-03-14 Neelakantan Padmanabhan

Model Order Reduction (MOR) methods enable the generation of real-time-capable digital twins, which can enable various novel value streams in industry. While traditional projection-based methods are robust and accurate for linear problems,…

Numerical Analysis · Mathematics 2021-09-09 Qinyu Zhuang , Juan Manuel Lorenzi , Hans-Joachim Bungartz , Dirk Hartmann

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

Numerical Analysis · Mathematics 2022-06-08 Alexander V. Mamonov , Maxim A. Olshanskii

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…

Numerical Analysis · Mathematics 2024-10-07 Diana A. Bistrian

Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…

Numerical Analysis · Mathematics 2021-09-14 Neeraj Sarna , Peter Benner

Linear reduced-order modeling (ROM) is widely used for efficient simulation of deformation dynamics, but its accuracy is often limited by the fixed linearization of the reduced mapping. We propose a new adaptive strategy for linear ROM that…

Graphics · Computer Science 2025-10-01 Yutian Tao , Maurizio Chiaramonte , Pablo Fernandez

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

Dynamical Systems · Mathematics 2026-03-19 Akira Saito , Masato Tanaka

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

Numerical Analysis · Mathematics 2020-11-24 Nikolaj T. Mücke , Sander M. Bohté , Cornelis W. Oosterlee

For a nonlinear dynamical system that depends on parameters, the paper introduces a novel tensorial reduced-order model (TROM). The reduced model is projection-based, and for systems with no parameters involved, it resembles proper…

Numerical Analysis · Mathematics 2023-11-16 Alexander V. Mamonov , Maxim A. Olshanskii

This paper proposes a data-driven algorithm for model order reduction (MOR) of large-scale wind farms and studies the effects that the obtained reduced-order model (ROM) has when this is integrated into the power grid. With respect to…

Systems and Control · Electrical Eng. & Systems 2024-12-16 Zilong Gong , Junyu Mao , Adrià Junyent-Ferré , Giordano Scarciotti

This paper introduces a novel data-driven convergence booster that not only accelerates convergence but also stabilizes solutions in cases where obtaining a steady-state solution is otherwise challenging. The method constructs a…

Fluid Dynamics · Physics 2025-04-09 Xukun Wang , Yilang Liu , Xiang Yang , Weiwei Zhang

Optimization problems arise in a range of scenarios, from optimal control to model parameter estimation. In many applications, such as the development of digital twins, it is essential to solve these optimization problems within…

Optimization and Control · Mathematics 2025-09-01 Joseph Hart , Shane A. McQuarrie , Zachary Morrow , Bart van Bloemen Waanders

Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many…

Computational Physics · Physics 2019-12-20 Sheroze Sheriffdeen , Jean C. Ragusa , Jim E. Morel , Marvin L. Adams , Tan Bui-Thanh

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

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

Numerical Analysis · Mathematics 2023-08-08 Giuseppe Carere , Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza , Rob Stevenson

The cost- and memory-efficient numerical simulation of coupled volume-based multi-physics problems like flow, transport, wave propagation and others remains a challenging task with finite element method (FEM) approaches. Goal-oriented space…

Mathematical Software · Computer Science 2019-05-01 Uwe Köcher , Marius Paul Bruchhäuser , Markus Bause

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

Numerical Analysis · Mathematics 2021-10-18 Zhongjian Wang , Wenlong Zhang , Zhiwen Zhang