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In this work we recast parametrized time dependent optimal control problems governed by partial differential equations in a saddle point formulation and we propose reduced order methods as an effective strategy to solve them. Indeed, on one…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Optimization and Control · Mathematics 2025-05-16 Matteo Tomasetto , Andrea Manzoni , Francesco Braghin

This work studies reduced order modeling (ROM) approaches to speed up the solution of variational data assimilation problems with large scale nonlinear dynamical models. It is shown that a key requirement for a successful reduced order…

Systems and Control · Computer Science 2015-05-20 Răzvan Ştefănescu , Adrian Sandu , Ionel Michael Navon

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Machine Learning · Computer Science 2026-01-16 Andrew F. Ilersich , Kevin Course , Prasanth B. Nair

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

Optimization and Control · Mathematics 2024-04-04 Wei Gong , Dongdong Liang

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional. For the numerical treatment, we use variational discretization of its Tikhonov regularization: For the state and the…

Optimization and Control · Mathematics 2017-12-08 Nikolaus von Daniels , Michael Hinze

In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…

Numerical Analysis · Mathematics 2024-01-22 Maria Strazzullo , Fabio Vicini

In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…

Numerical Analysis · Mathematics 2017-12-22 Bangti Jin , Buyang Li , Zhi Zhou

This paper presents a pressure-robust discretizations, specifically within the context of optimal control problems for the Stokes-Darcy system. The study meticulously revisits the formulation of the divergence constraint and the enforcement…

Numerical Analysis · Mathematics 2025-02-25 Jingshi Li , Jiachuan Zhang , Ran Zhang

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Renzo Mosetti , Gianluigi Rozza

We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…

Numerical Analysis · Mathematics 2025-12-11 Christos Pervolianakis

In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…

Numerical Analysis · Mathematics 2024-02-21 Ivan Prusak , Davide Torlo , Monica Nonino , Gianluigi Rozza

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2024-12-30 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

In this paper we investigate a priori error estimates for the space-time Galerkin finite element discretization of an optimal control problem governed by a simplified linear gradient enhanced damage model. The model equations are of a…

Numerical Analysis · Mathematics 2020-04-10 Marita Holtmannspötter , Arnd Rösch , Boris Vexler

This paper presents a space-time finite element method (FEM) based on an unfitted mesh for solving parabolic problems on moving domains. Unlike other unfitted space-time finite element approaches that commonly employ the discontinuous…

Numerical Analysis · Mathematics 2026-04-03 Ruizhi Wang , Weibing Deng

This work investigates projection-based Reduced-Order Models (ROMs) formulated in the frequency domain, employing a space-time basis constructed with Spectral Proper Orthogonal Decomposition to efficiently represent dominant spatio-temporal…

Fluid Dynamics · Physics 2026-01-12 Xiaodong Li , Davide Lasagna

This article presents a Galerkin projection-based reduced-order modelling (ROM) approach for segregated fluid-structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian Eulerian (ALE) framework at low Reynolds numbers…

Numerical Analysis · Mathematics 2025-07-24 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

We study the effect of the streamline upwind/Petrov Galerkin (SUPG) stabilized finite element method on the discretization of optimal control problems governed by linear advection-diffusion equations. We compare two approaches for the…

Numerical Analysis · Mathematics 2024-11-18 S. Scott Collis , Matthias Heinkenschloss

We introduce reduced order methods as an efficient strategy to solve parametrized non-linear and time dependent optimal flow control problems governed by partial differential equations. Indeed, the optimal control problems require a huge…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Zakia Zainib , Francesco Ballarin , Gianluigi Rozza