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This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied…

Numerical Analysis · Computer Science 2015-06-18 Răzvan Ştefănescu , Adrian Sandu , Ionel M. Navon

Accurate reconstruction of ocean is essential for reflecting global climate dynamics and supporting marine meteorological research. Conventional methods face challenges due to sparse data, algorithmic complexity, and high computational…

Computer Vision and Pattern Recognition · Computer Science 2025-06-13 Yuanyi Song , Pumeng Lyu , Ben Fei , Fenghua Ling , Wanli Ouyang , Lei Bai

In this study, an efficient reanalysis strategy for dynamic topology optimization is proposed. Compared with other related studies, an online successive dynamic reanalysis method and POD-based approximate dynamic displacement strategy are…

Numerical Analysis · Mathematics 2023-05-16 Shuhao Li , Hu Wang , Jichao Yin , Daozhen Guo , Guangyao Li

While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…

Numerical Analysis · Mathematics 2025-08-13 Sebastiaan P. C. van Schie , Boris Kramer , John T. Hwang

Within the environmental context, numerical modeling is a promising approach to assessing the energy efficiency of buildings. Resilient buildings need to be designed, and capable of adapting to future extreme heat. Simulations are required…

Computational Engineering, Finance, and Science · Computer Science 2022-06-20 Julien Berger , Cyrille Allery , Anaïs Machard

The aim of this work was to predict the probability of the spread of rock formations with hydrocarbon-collecting properties in the studied coastal area using a stack of machine learning algorithms and data augmentation and modification…

Geophysics · Physics 2023-01-10 Dmitry Ivlev

Accurate reconstruction of temperature field of heat-source systems (TFR-HSS) is crucial for thermal monitoring and reliability assessment in engineering applications such as electronic devices and aerospace structures. However, the high…

Machine Learning · Computer Science 2025-12-02 Shihang Li , Zhiqiang Gong , Weien Zhou , Yue Gao , Wen Yao

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

Numerical Analysis · Mathematics 2025-04-28 Bosco García-Arcilla , Alicia García-Mascaraque , Julia Novo

This paper addresses the challenges of thermal sensor allocation and full-chip temperature reconstruction in multi-core systems by leveraging an entropy-based sensor placement strategy and an adaptive compressive sensing approach. By…

Systems and Control · Electrical Eng. & Systems 2026-01-13 Kun-Chih , Chen , Chia-Hsin Chen , Lei-Qi Wang , Chun-Chieh Wang

The detailed knowledge of the inner skin temperature behavior is very important to evaluate and manage the aging of large pipes in cooling systems. We describe here a method to obtain this information as a function of outer skin temperature…

Computational Physics · Physics 2014-04-30 Jean-Philippe Argaud , Bertrand Bouriquet , Aimery Assire , Stéphane Gervais

Achieving thermal comfort while maintaining energy efficiency is a critical objective in building system control. Conventional thermal comfort models, such as the Predicted Mean Vote (PMV), rely on both environmental and personal variables.…

Computational Engineering, Finance, and Science · Computer Science 2025-11-06 Youngkyu Kim , Byounghyun Yoo , Ji Young Yun , Hyeokmin Lee , Sehyeon Park , Jin Woo Moon , Eun Ji Choi

Central to Earth observation is the trade-off between spatial and temporal resolution. For temperature, this is especially critical because real-world applications require high spatiotemporal resolution data. Current technology allows for…

Image and Video Processing · Electrical Eng. & Systems 2025-07-15 Shengjie Liu , Lu Zhang , Siqin Wang

In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper…

Computational Physics · Physics 2025-07-29 Lidong Fang , Zilong Song , Kirk Fraser , Faisal Habib , Christopher Drummond , Huaxiong Huang

We propose a data-driven algorithm for reconstructing the irregular, chaotic flow dynamics around two side-by-side square cylinders from sparse, time-resolved, velocity measurements in the wake. We use Proper Orthogonal Decomposition (POD)…

Fluid Dynamics · Physics 2022-09-08 Flavio Savarino , George Papadakis

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

Perception of the full state is an essential technology to support the monitoring, analysis, and design of physical systems, one of whose challenges is to recover global field from sparse observations. Well-known for brilliant approximation…

Artificial Intelligence · Computer Science 2023-02-21 Xiaoyu Zhao , Xiaoqian Chen , Zhiqiang Gong , Weien Zhou , Wen Yao , Yunyang Zhang

A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…

Numerical Analysis · Mathematics 2012-07-23 Muriel Boulakia , Elisa Schenone , Jean-Frédéric Gerbeau

Multiscale modeling and analysis of multiphysics coupling processes in highly heterogeneous media present significant challenges. In this paper, we propose a novel multiphysics embedding localized orthogonal decomposition (ME-LOD) method…

Numerical Analysis · Mathematics 2025-07-21 Yuzhou Nan , Yajun Wang , Changqing Ye , Xiaofei Guan

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

Hall thrusters are susceptible to large-amplitude plasma oscillations that impact thruster performance and lifetime and are also difficult to model. High-speed cameras are a popular tool to study these dynamics due to their spatial…

Plasma Physics · Physics 2022-05-31 J. W. Brooks , M. S. McDonald , A. A. Kaptanoglu