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Machine learning and artificial intelligence algorithms typically require large amount of data for training. This means that for nonlinear aeroelastic applications, where small training budgets are driven by the high computational burden…

Space-Time Projection (STP) is introduced as a data-driven forecasting approach for high-dimensional and time-resolved data. The method computes extended space-time proper orthogonal modes from training data spanning a prediction horizon…

Machine Learning · Computer Science 2025-04-01 Oliver T. Schmidt

We propose a novel stochastic reduced-order model (SROM) for complex systems by combining clustering and classification strategies. Specifically, the distance and centroid of centroidal Voronoi tessellation (CVT) are redefined according to…

Numerical Analysis · Mathematics 2022-04-26 Meixin Xiong , Liuhong Chen , Ju Ming , Zhiwen Zhang

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

This work investigates model reduction techniques for nonlinear parameterized and time-dependent PDEs, specifically focusing on bifurcating phenomena in Computational Fluid Dynamics (CFD). We develop interpretable and non-intrusive Reduced…

Numerical Analysis · Mathematics 2025-12-01 Lorenzo Tomada , Moaad Khamlich , Federico Pichi , Gianluigi Rozza

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

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

Numerical Analysis · Mathematics 2023-05-09 Simone Brivio , Stefania Fresca , Nicola Rares Franco , Andrea Manzoni

We developed a novel reduced-order multi-scale method for solving large time-domain wavefield simulation problems. Our algorithm consists of two main stages. During the first "off-line" stage the fine-grid operator (of the graph Laplacian…

Numerical Analysis · Mathematics 2017-03-28 Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

Reduced order methods (ROMs) for the incompressible Navier--Stokes equations, based on proper orthogonal decomposition (POD), are studied that include snapshots which approach the temporal derivative of the velocity from a full order mixed…

Numerical Analysis · Mathematics 2023-04-18 Bosco García-Archilla , Volker John , Sarah Katz , Julia Novo

This paper presents a new technique for developing reduced-order models (ROMs) for nonlinear radiative transfer problems in high-energy density physics. The proper orthogonal decomposition (POD) of photon intensities is applied to obtain…

Numerical Analysis · Mathematics 2026-03-18 Joseph M. Coale , Dmitriy Y. Anistratov

Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal…

Machine Learning · Computer Science 2025-12-24 Shane X. Coffing , John Tipton , Arvind T. Mohan , Darren Engwirda

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…

Numerical Analysis · Mathematics 2016-02-17 Alessandro Alla , J. Nathan Kutz

We propose a technique for performing spectral (in time) analysis of spatially-resolved flowfield data, without needing any temporal resolution or information. This is achieved by combining projection-based reduced-order modeling with…

Fluid Dynamics · Physics 2023-07-31 Katherine J. Asztalos , Abdulrahman Almashjary , Scott T. M. Dawson

Many applications in computational physics involve approximating problems with microstructure, characterized by multiple spatial scales in their data. However, these numerical solutions are often computationally expensive due to the need to…

Numerical Analysis · Mathematics 2023-09-15 Piermario Vitullo , Alessio Colombo , Nicola Rares Franco , Andrea Manzoni , Paolo Zunino

Transport-dominated phenomena provide a challenge for common mode-based model reduction approaches. We present a model reduction method, which is suited for these kind of systems. It extends the proper orthogonal decomposition (POD) by…

Numerical Analysis · Mathematics 2018-02-20 Julius Reiss , Philipp Schulze , Jörn Sesterhenn , Volker Mehrmann

Reduced-order models (ROMs) are widely used in fluid engineering to enable rapid prediction of flow fields for parametric analysis, design optimization, and control applications. Proper orthogonal decomposition (POD) is commonly employed to…

Fluid Dynamics · Physics 2026-02-25 Yuto Nakamura , Shintaro Sato , Naofumi Ohnishi

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor)…

Numerical Analysis · Mathematics 2024-09-24 Joseph M. Coale , Dmitriy Y. Anistratov

Projection-based Reduced Order Models (ROMs) are often deployed as static surrogates, which limits their practical utility once a system leaves the training manifold. We formalize and study adaptive non-intrusive ROMs that update both the…

Machine Learning · Computer Science 2026-02-13 Amirpasha Hedayat , Alberto Padovan , Karthik Duraisamy

This paper presents a projection-based reduced order modelling (ROM) framework for unsteady parametrized optimal control problems (OCP$_{(\mu)}$s) arising from cardiovascular (CV) applications. In real-life scenarios, accurately defining…

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