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Strong correlations between explanatory variables are problematic for high-dimensional regularized regression methods. Due to the violation of the Irrepresentable Condition, the popular LASSO method may suffer from false inclusions of…

Methodology · Statistics 2021-06-18 Xu Han , Ethan X Fang , Cheng Yong Tang

Predicting and perhaps mitigating against rare, extreme events in fluid flows is an important challenge. Due to the time-localised nature of these events, Fourier-based methods prove inefficient in capturing them. Instead, this paper uses…

Fluid Dynamics · Physics 2024-12-05 Anagha Madhusudanan , Rich R. Kerswell

Reduced-order models are essential tools to deal with parametric problems in the context of optimization, uncertainty quantification, or control and inverse problems. The set of parametric solutions lies in a low-dimensional manifold (with…

Numerical Analysis · Mathematics 2021-04-29 Pedro Díez , Alba Muixí , Sergio Zlotnik , Alberto García-González

This study focuses on the stratification patterns and dynamic evolution of reservoir water temperatures, aiming to estimate and reconstruct the temperature field using limited and noisy local measurement data. Due to complex measurement…

Machine Learning · Computer Science 2025-02-21 Qianyu He , Huaiwei Sun , Yubo Li , Zhiwen You , Qiming Zheng , Yinghan Huang , Sipeng Zhu , Fengyu Wang

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

Energy transfer across scales is fundamental in fluid dynamics, linking large-scale flow motions to small-scale turbulent structures in engineering and natural environments. Triadic interactions among three wave components form complex…

Fluid Dynamics · Physics 2024-11-21 Brandon Yeung , Tianyi Chu , Oliver T. Schmidt

Quantum computing is a promising technology for accelerating partial differential equation solvers applied to large-scale real-world problems. However, reconstructing a classical representation of the solution from the quantum state remains…

We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…

Numerical Analysis · Mathematics 2019-05-15 Marco Tezzele , Nicola Demo , Gianluigi Rozza

In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal…

Dynamical Systems · Mathematics 2016-05-04 Dan Yu , Suman Chakravorty

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Fluid Dynamics · Physics 2021-11-24 Stefania Fresca , Andrea Manzoni

Parametric model order reduction techniques often struggle to accurately represent transport-dominated phenomena due to a slowly decaying Kolmogorov n-width. To address this challenge, we propose a non-intrusive, data-driven methodology…

Fluid Dynamics · Physics 2023-05-01 Shubhaditya Burela , Philipp Krah , Julius Reiss

Modal decomposition of turbulent flows using classical proper orthogonal decomposition (POD) often suffers from mode mixing, in which a distinct coherent structure may be distributed over several POD modes. We propose a decomposition method…

Fluid Dynamics · Physics 2026-05-12 Eman Bagheri , Riccardo Casali , Stefan Becker , Philipp Schlatter

Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science…

Numerical Analysis · Mathematics 2020-02-19 Hannah Lu , Daniel M. Tartakovsky

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…

Numerical Analysis · Mathematics 2022-11-01 Bosco García-Archilla , Volker John , Julia Novo

In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…

Particle advection is one of the foundational algorithms for visualization and analysis and is central to understanding vector fields common to scientific simulations. Achieving efficient performance with large data in a distributed memory…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-15 Zhe Wang , Kenneth Moreland , Matthew Larsen , James Kress , Hank Childs , David Pugmire

We present a framework for parametric proper orthogonal decomposition (POD)-Galerkin reduced-order modeling (ROM) of fluid flows that accommodates variations in flow parameters and control inputs. As an initial step, to explore how the…

Fluid Dynamics · Physics 2025-11-10 Shintaro Sato , Oliver T. Schmidt

High-performance computing enables simulation of high-dimensional physical systems, but downstream analyses such as inverse problems and control remain computationally expensive, motivating model order reduction (MOR) to construct efficient…

Fluid Dynamics · Physics 2026-05-28 Tomoki Koike , Prakash Mohan , Marc T. Henry de Frahan , Elizabeth Qian , Julie Bessac

A data-driven algorithm is proposed that employs sparse data from velocity and/or scalar sensors to forecast the future evolution of three dimensional turbulent flows. The algorithm combines time-delayed embedding together with Koopman…

Fluid Dynamics · Physics 2026-03-04 George Papadakis , Shengqi Lu

We present the Super-Localized Orthogonal Decomposition (SLOD) method for the numerical homogenization of linear elasticity problems with multiscale microstructures modeled by a heterogeneous coefficient field without any periodicity or…

Numerical Analysis · Mathematics 2025-01-10 Camilla Belponer , José C. Garay , Peter Munch , Daniel Peterseim