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Stepwise controllable devices, such as switched capacitors or stepwise controllable loads and generators, transform the nonconvex AC optimal power flow (AC-OPF) problem into a nonconvex mixed-integer (MI) programming problem which is…

Optimization and Control · Mathematics 2025-10-13 Johannes Heid , Nils Bornhorst , Eric Tönges , Philipp Härtel , Denis Mende , Martin Braun

In this paper we utilize the Proper Orthogonal Decomposition (POD) method for model order reduction in application to Smoluchowski aggregation equations with source and sink terms. In particular, we show in practice that there exists a…

Numerical Analysis · Mathematics 2024-03-06 Ivan V. Timokhin , Sergey A. Matveev , Eugene E. Tyrtyshnikov , Alexander P. Smirnov

The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures…

Fluid Dynamics · Physics 2016-04-20 Moritz Sieber , Kilian Oberleithner , Christian Oliver Paschereit

In this article, we propose a two-grid based adaptive proper orthogonal decomposition (POD) method to solve the time dependent partial differential equations. Based on the error obtained in the coarse grid, we propose an error indicator for…

Numerical Analysis · Mathematics 2020-07-24 Xiaoying Dai , Xiong Kuang , Jack Xin , Aihui Zhou

We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to…

Optimization and Control · Mathematics 2009-11-13 Miloš Ilak , Clarence W. Rowley

We consider the frequency domain form of proper orthogonal decomposition (POD) called spectral proper orthogonal decomposition (SPOD). Spectral POD is derived from a space-time POD problem for statistically stationary flows and leads to…

Fluid Dynamics · Physics 2018-06-05 Aaron Towne , Oliver T. Schmidt , Tim Colonius

Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…

Fluid Dynamics · Physics 2026-05-28 Shan Ding , Yongfu Tian , Rui Yang

Mean-field variational inference (MFVI) is a widely used method for approximating high-dimensional probability distributions by product measures. It has been empirically observed that MFVI optimizers often suffer from mode collapse.…

Machine Learning · Statistics 2025-10-21 Shunan Sheng , Bohan Wu , Alberto González-Sanz

Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…

Optimization and Control · Mathematics 2023-11-29 Sergey Dolgov , Dante Kalise , Luca Saluzzi

A model-order reduction framework for the meshless smoothed-particle hydrodynamics (SPH) method is presented. The proposed framework introduces the concept of modal reference spaces to overcome the challenges of discovering low-dimensional…

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

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

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

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

Numerical Analysis · Mathematics 2020-11-23 Charumathi V , M. Ramakrishna , Vinita Vasudevan

In this paper, we propose a computationally efficient iterative algorithm for proper orthogonal decomposition (POD) using random sampling based techniques. In this algorithm, additional rows and columns are sampled and a merging technique…

Numerical Analysis · Computer Science 2021-07-07 V. Charumathi , M. Ramakrishna , Vinita Vasudevan

We consider integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion equations. The drift-diffusion equations are discretized in space using mixed finite element method. This discretization yields a…

Numerical Analysis · Mathematics 2010-03-03 Michael Hinze , Martin Kunkel

We introduce MoTIF, a mode-structured tensor framework for multi-parametric approximation, super-resolution, and temporal forecasting of high-dimensional unsteady systems. The methodology leverages High-Order Singular Value Decomposition…

In the present work, we introduce a data-driven approach to enhance the accuracy of non-intrusive Reduced Order Models (ROMs). In particular, we focus on ROMs built using Proper Orthogonal Decomposition (POD) in an under-resolved and…

Numerical Analysis · Mathematics 2026-05-26 Gabriele Codega , Anna Ivagnes , Nicola Demo , Gianluigi Rozza

Classical neural ordinary differential equations (ODEs) are powerful tools for approximating the log-density functions in high-dimensional spaces along trajectories, where neural networks parameterize the velocity fields. This paper…

Optimization and Control · Mathematics 2025-01-30 Mo Zhou , Stanley Osher , Wuchen Li

Deep learning-based methods have achieved encouraging performances in the field of magnetic resonance (MR) image reconstruction. Nevertheless, to properly learn a powerful and robust model, these methods generally require large quantities…

Image and Video Processing · Electrical Eng. & Systems 2023-04-18 Ruoyou Wu , Cheng Li , Juan Zou , Qiegen Liu , Hairong Zheng , Shanshan Wang