Related papers: POD-based reduced order methods for optimal contro…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method,…
A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
In this work, a numerical simulation of 1D Burgers' equation is developed using finite difference method and a reduced order model (ROM) of the simulation is developed using proper orthogonal decomposition (POD). The objective of this work…
We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…
We address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlling the unknown system. We assume that the desired PDE is…
We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…
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…
In PDE-constrained optimization, proper orthogonal decomposition (POD) provides a surrogate model of a (potentially expensive) PDE discretization, on which optimization iterations are executed. Because POD models usually provide good…
Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…
This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…
We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional…
We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code…
The present work considers the optimal control of a convective Cahn-Hilliard system, where the control enters through the velocity in the transport term. We prove the existence of a solution to the considered optimal control problem. For an…
Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…