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This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive `error indicators'…

Numerical Analysis · Computer Science 2015-04-16 Martin Drohmann , Kevin Carlberg

The use of Internet of Things (IoT) technologies is becoming a preferred solution for the assessment of tailings dams' safety. Real-time sensor monitoring proves to be a key tool for reducing the risk related to these ever-evolving…

Computational Engineering, Finance, and Science · Computer Science 2021-06-08 Christina Nasikaa , Pedro Diez , Pierre Gerard , Thierry J. Massart , Sergio Zlotnik

It is expensive to compute residual diffusivity in chaotic in-compressible flows by solving advection-diffusion equation due to the formation of sharp internal layers in the advection dominated regime. Proper orthogonal decomposition (POD)…

Computational Physics · Physics 2019-10-02 Jiancheng Lyu , Jack Xin , Yifeng Yu

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Numerical Analysis · Mathematics 2024-05-15 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino , Jan S. Hesthaven

In this manuscript, we combine non-intrusive reduced order models (ROMs) with space-dependent aggregation techniques to build a mixed-ROM. The prediction of the mixed formulation is given by a convex linear combination of the predictions of…

Numerical Analysis · Mathematics 2024-03-12 Anna Ivagnes , Niccolò Tonicello , Paola Cinnella , Gianluigi Rozza

The numerical approximation of convection-dominated problems continues to remain subject of strong interest. Families of stabilization techniques for finite element methods were developed in the past. Adaptive techniques based on a…

Numerical Analysis · Mathematics 2018-03-20 Kristina Schwegler , Marius P. Bruchhäuser , Markus Bause

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…

The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…

Computational Engineering, Finance, and Science · Computer Science 2024-10-14 T. Guo , V. G. Kouznetsova , M. G. D. Geers , K. Veroy , O. Rokoš

In this work, we focus on reduced order modeling (ROM) techniques for hyperbolic conservation laws with application in uncertainty quantification (UQ) and in conjunction with the well-known Monte Carlo sampling method. Because we are…

Numerical Analysis · Mathematics 2018-08-13 R. Crisovan , D. Torlo , R. Abgrall , S. Tokareva

We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient…

Numerical Analysis · Mathematics 2021-04-14 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…

Numerical Analysis · Mathematics 2023-07-04 Jun Sur Richard Park , Xueyu Zhu

An adaptive scheme to generate reduced-order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD-Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively…

Numerical Analysis · Mathematics 2021-10-13 Sridhar Chellappa , Lihong Feng , Peter Benner

Convection-dominated problems are known for their slow Kolmogorov $n$-width decays and are challenging for model order reduction (MOR). In this work, we propose a hybrid surrogate modeling approach and a non-intrusive variant that overcome…

Dynamical Systems · Mathematics 2026-05-29 Lihong Feng , Ali Hassan , Shuwen Sun

Kinetic equations are crucial for modeling non-equilibrium phenomena, but their computational complexity is a challenge. This paper presents a data-driven approach using reduced order models (ROM) to efficiently model non-equilibrium flows…

Fluid Dynamics · Physics 2023-10-09 Julian Koellermeier , Philipp Krah , Julius Reiss , Zachary Schellin

We present a reduced-order model (ROM) methodology for inverse scattering problems in which the reduced-order models are data-driven, i.e. they are constructed directly from data gathered by sensors. Moreover, the entries of the ROM contain…

Numerical Analysis · Mathematics 2023-06-16 Jörn Zimmerling , Vladimir Druskin , Murthy Guddati , Elena Cherkaev , Rob Remis

A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in…

General Relativity and Quantum Cosmology · Physics 2018-06-11 Dániel Barta , Mátyás Vasúth

Model order reduction (MOR) has long been a mainstream strategy to accelerate large-scale transient circuit simulation. Dynamic Mode Decomposition (DMD) represents a novel data-driven characterization method, extracting dominant dynamical…

Signal Processing · Electrical Eng. & Systems 2025-08-06 Na Liu , Chengliang Dai , Qiuyue Wu , Qiuqi Li , Guoxiong Cai

The objective of this paper is to develop a global non-intrusive Parametric Model Order Reduction (PMOR) methodology for the problem of changing well locations in an oil field, that can eventually be used for well placement optimization to…

Computational Engineering, Finance, and Science · Computer Science 2020-01-16 Hardikkumar Zalavadia , Eduardo Gildin

Data-driven modal decompositions are useful tools for compressing data or identifying dominant structures. Popular ones like the dynamic mode decomposition (DMD) and the proper orthogonal decomposition (POD) are defined with continuous…

Fluid Dynamics · Physics 2025-11-06 Manuel Ratz , Alessandro Parente , Miguel Alfonso Mendez

This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are…

Numerical Analysis · Mathematics 2017-12-04 Matthias Maier , Rolf Rannacher