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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

In this paper infinite horizon optimal control problems for nonlinear high-dimensional dynamical systems are studied. Nonlinear feedback laws can be computed via the value function characterized as the unique viscosity solution to the…

Optimization and Control · Mathematics 2016-02-22 Alessandro Alla , Maurizio Falcone , Stefan Volkwein

In this paper, we consider the problem of model reduction of large scale systems, such as those obtained through the discretization of PDEs. We propose a randomized proper orthogonal decomposition (RPOD) technique to obtain the reduced…

Dynamical Systems · Mathematics 2013-12-17 Dan Yu , Suman Chakravorty

We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D…

Numerical Analysis · Mathematics 2026-03-20 Rahul Halder , Arash Hajisharifi , Kabir Bakhshaei , Gianluigi Rozza

In this paper we study the approximation of an optimal control problem for linear para\-bolic PDEs with model order reduction based on Proper Orthogonal Decomposition (POD-MOR). POD-MOR is a Galerkin approach where the basis functions are…

Optimization and Control · Mathematics 2016-09-01 Alessandro Alla , Carmen Graessle , Michael Hinze

The increasing size and complexity of modern power systems have led to a high-dimensional mathematical model for transient stability studies, rendering full-scale simulations computationally burdensome. While dimensionality reduction is…

Dynamical Systems · Mathematics 2025-12-08 Farhana Farooq , Danish Rafiq

In this report we present the approximation of an infinite horizon optimal control problem for the evolutive Navier-Stokes system. The method is based on a model reduction technique, using a POD approximation, coupled with a Hamilton-Jacobi…

Numerical Analysis · Mathematics 2014-05-07 Alessandro Alla , Michael Hinze

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

We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…

Numerical Analysis · Mathematics 2022-02-22 Gobat G. , Opreni A. , Fresca S. , Manzoni A. , Frangi A

We present a framework for optimal trajectory generation in flow-driven systems governed by the Navier-Stokes equations, combining a Proper Orthogonal Decomposition (POD) reduced0order model (ROM) with Model Predictive Control (MPC). The…

Optimization and Control · Mathematics 2025-12-01 Adam Waterman , Martin Guay

In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…

Optimization and Control · Mathematics 2020-12-15 Sebastian Peitz , Stefan Klus

Recent research in non-intrusive data-driven model order reduction (MOR) enabled accurate and efficient approximation of parameterized ordinary differential equations (ODEs). However, previous studies have focused on constant parameters,…

Dynamical Systems · Mathematics 2021-10-27 Jonas Kneifl , Julian Hay , Jörg Fehr

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

Numerical Analysis · Mathematics 2017-09-28 Max Gunzburger , Nan Jiang , Michael Schneier

We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…

Optimization and Control · Mathematics 2015-05-21 Tuğba Akman

We propose a space-time reduced-order model (ROM) for nonlinear dynamical systems, building upon previous work on linear systems. Whereas most ROMs are space-only in that they reduce only the spatial dimension of the state, the proposed…

Numerical Analysis · Mathematics 2025-11-03 Peter Frame , Aaron Towne

We propose a data-driven model order reduction (MOR) technique for parametrized partial differential equations that exhibit parameter-dependent jump-discontinuities. Such problems have poor-approximability in a linear space and therefore,…

Numerical Analysis · Mathematics 2021-05-04 Neeraj Sarna , Peter Benner

Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…

The main focus of the present work is the inclusion of spatial adaptivity for the snapshot computation in the offline phase of model order reduction utilizing Proper Orthogonal Decomposition (POD-MOR) for nonlinear parabolic evolution…

Numerical Analysis · Mathematics 2020-08-04 Carmen Gräßle , Michael Hinze

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

This contribution proposes novel data-driven surrogate modeling approaches for parameterized parabolic PDEs, where the parameter dependence can be split into two parts with different decay behavior of the Kolmogorov $N$-width. Such problems…

Numerical Analysis · Mathematics 2026-04-27 Dawid Kotowski , Mario Ohlberger