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This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…

Optimization and Control · Mathematics 2023-02-20 Xiaodong Cheng

We provide first the functional analysis background required for reduced order modeling and present the underlying concepts of reduced basis model reduction. The projection-based model reduction framework under affinity assumptions,…

Numerical Analysis · Mathematics 2023-08-30 Gianluigi Rozza , Martin Hess , Giovanni Stabile , Marco Tezzele , Francesco Ballarin

We consider a sketched implementation of the finite element method for elliptic partial differential equations on high-dimensional models. Motivated by applications in real-time simulation and prediction we propose an algorithm that…

Numerical Analysis · Mathematics 2020-04-22 Robert Lung , Yue Wu , Dimitris Kamilis , Nick Polydorides

This paper presents a projection-based reduced order modelling (ROM) framework for unsteady parametrized optimal control problems (OCP$_{(\mu)}$s) arising from cardiovascular (CV) applications. In real-life scenarios, accurately defining…

This paper proposes a non-intrusive, data-driven reduced-order modeling framework for stochastic optimal control problems governed by partial differential equations. The control problem is formulated with a quadratic cost functional and…

Optimization and Control · Mathematics 2026-05-20 Lingling Ma , Jingyi Zhang , Qiuqi Li

A slow decaying Kolmogorov n-width of the solution manifold of a parametric partial differential equation precludes the realization of efficient linear projection-based reduced-order models. This is due to the high dimensionality of the…

Numerical Analysis · Mathematics 2023-08-08 Francesco Romor , Giovanni Stabile , Gianluigi Rozza

Non-intrusive reduced-order modeling techniques are necessary for systems that are simulated using black-box solvers or known only from data. For systems exhibiting large transients and operating far away from equilibria, current…

Numerical Analysis · Mathematics 2026-03-24 Cole J. Errico , Alberto Padovan , Daniel J. Bodony

Accurate and inexpensive Reduced Order Models (ROMs) for forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control in engineering problems. Galerkin projection based Reduced Order…

Fluid Dynamics · Physics 2023-01-27 Surya Chakrabarti , Arvind T. Mohan , Datta V. Gaitonde , Daniel Livescu

A data-driven closure modeling based on proper orthogonal decomposition (POD) temporal modes is used to obtain stable and accurate reduced order models (ROMs) of unsteady compressible flows. Model reduction is obtained via Galerkin and…

Fluid Dynamics · Physics 2021-09-22 Victor Zucatti , William Wolf

In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular…

Machine Learning · Computer Science 2020-03-03 Lin Chen , Mingrui Zhang , Hamed Hassani , Amin Karbasi

Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…

Numerical Analysis · Mathematics 2026-03-27 Lijie Ji , Sabrina Rashid , Yanlai Chen , Zhu Wang

This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…

Machine Learning · Statistics 2024-11-08 Jin Yi Yong , Rudy Geelen , Johann Guilleminot

Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible flow around a circular cylinder is presented in this work. The ROM…

Numerical Analysis · Mathematics 2018-02-06 Giovanni Stabile , Saddam Hijazi , Andrea Mola , Stefano Lorenzi , Gianluigi Rozza

We introduce a novel approach for analyzing the performance of first-order black-box optimization methods. We focus on smooth unconstrained convex minimization over the Euclidean space $R^d$. Our approach relies on the observation that by…

Optimization and Control · Mathematics 2012-06-15 Yoel Drori , Marc Teboulle

This work introduces a novel blackbox optimization algorithm for computationally expensive constrained multi-fidelity problems. When applying a direct search method to such problems, the scarcity of feasible points may lead to numerous…

Optimization and Control · Mathematics 2025-04-09 Stéphane Alarie , Charles Audet , Miguel Diago , Sébastien Le Digabel , Xavier Lebeuf

A methodology for using random sketching in the context of model order reduction for high-dimensional parameter-dependent systems of equations was introduced in [Balabanov and Nouy 2019, Part I]. Following this framework, we here construct…

Numerical Analysis · Mathematics 2022-03-25 Oleg Balabanov , Anthony Nouy

This thesis presents recent advances in model order reduction methods with the primary aim to construct online-efficient reduced surrogate models for parameterized multiscale phenomena and accelerate large-scale PDE-constrained parameter…

Numerical Analysis · Mathematics 2022-11-18 Tim Keil

In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM)…

Numerical Analysis · Mathematics 2024-08-27 Fabio Zoccolan , Maria Strazzullo , Gianluigi Rozza

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

In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization,…

Numerical Analysis · Mathematics 2023-08-08 Matteo Zancanaro , Francesco Ballarin , Simona Perotto , Gianluigi Rozza