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In real-world scenarios, complex data such as multispectral images and multi-frame videos inherently exhibit robust low-rank property. This property is vital for multi-dimensional inverse problems, such as tensor completion, spectral…

Computer Vision and Pattern Recognition · Computer Science 2024-12-17 Xiangming Wang , Haijin Zeng , Jiaoyang Chen , Sheng Liu , Yongyong Chen , Guoqing Chao

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

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…

Systems and Control · Computer Science 2015-05-20 Răzvan Ştefănescu , Adrian Sandu , Ionel Michael Navon

In feedback flow control, one of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A…

Optimization and Control · Mathematics 2015-05-13 Zhanhua Ma , Sunil Ahuja , Clarence W. Rowley

This paper introduces a reduced-order modeling approach based on finite volume methods for hyperbolic systems, combining Proper Orthogonal Decomposition (POD) with the Discrete Empirical Interpolation Method (DEIM) and Proper Interval…

Numerical Analysis · Mathematics 2025-05-07 I. Gómez-Bueno , E. D. Fernández-Nieto , S. Rubino

Reduced-order models are central to motion planning and control of quadruped robots, yet existing templates are often hand-crafted for a specific locomotion modality. This motivates the need for automatic methods that extract task-specific,…

Robotics · Computer Science 2026-01-14 Gioele Buriani , Jingyue Liu , Maximilian Stölzle , Cosimo Della Santina , Jiatao Ding

Reduced order modelling relies on representing complex dynamical systems using simplified modes, which can be achieved through Koopman operator analysis. However, computing Koopman eigen pairs for high-dimensional observable data can be…

Dynamical Systems · Mathematics 2023-06-09 Neranjaka Jayarathne , Erik M. Bollt

We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…

Numerical Analysis · Mathematics 2014-11-03 Paul G. Constantine , David F. Gleich , Yangyang Hou , Jeremy Templeton

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

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

With the advancement of neural networks, there has been a notable increase, both in terms of quantity and variety, in research publications concerning the application of autoencoders to reduced-order models. We propose a polytopic…

Machine Learning · Computer Science 2024-10-30 Jan Heiland , Yongho Kim

Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…

Machine Learning · Computer Science 2025-10-23 Elias Al Ghazal , Jad Mounayer , Beatriz Moya , Sebastian Rodriguez , Chady Ghnatios , Francisco Chinesta

The complexity of state-of-the-art Transformer-based models for skeleton-based action recognition poses significant challenges in terms of computational efficiency and resource utilization. In this paper, we explore the application of…

Computer Vision and Pattern Recognition · Computer Science 2024-07-23 Soroush Oraki , Harry Zhuang , Jie Liang

We propose and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations. The first projection method is a generalization of the…

Numerical Analysis · Mathematics 2018-10-22 Olivier Zahm , Marie Billaud-Friess , Anthony Nouy

Most model reduction methods reduce the state dimension and then temporally evolve a set of coefficients that encode the state in the reduced representation. In this paper, we instead employ an efficient representation of the entire…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Cong Lin , Oliver Schmidt , Aaron Towne

As a major breakthrough in artificial intelligence and deep learning, Convolutional Neural Networks have achieved an impressive success in solving many problems in several fields including computer vision and image processing. Real-time…

Computer Vision and Pattern Recognition · Computer Science 2024-01-22 Laura Meneghetti , Nicola Demo , 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

Autoencoders are unsupervised deep learning models used for learning representations. In literature, autoencoders have shown to perform well on a variety of tasks spread across multiple domains, thereby establishing widespread…

Computer Vision and Pattern Recognition · Computer Science 2018-10-16 Maneet Singh , Shruti Nagpal , Mayank Vatsa , Richa Singh , Afzel Noore

In this article, we study eigenvalue problems associated to self-adjoint operators and their approximation obtained by subspace projection, as used in the reduced basis method for instance. We provide error bounds between the exact…

Mathematical Physics · Physics 2025-06-16 Louis Garrigue , Benjamin Stamm

Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…

Numerical Analysis · Mathematics 2022-03-02 Davide Papapicco , Nicola Demo , Michele Girfoglio , Giovanni Stabile , Gianluigi Rozza