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To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…

The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…

Reduced order modeling has gained considerable attention in recent decades owing to the advantages offered in reduced computational times and multiple solutions for parametric problems. The focus of this manuscript is the application of…

Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…

A variational framework, initially developed for high-order mesh optimisation, is being extended for r-adaptation. The method is based on the minimisation of a functional of the mesh deformation. To achieve adaptation, elements of the…

Parametric model order reduction (pMOR) is a powerful tool for accelerating finite element (FE) simulations while maintaining parametric dependencies. For geometric parameters, pMOR by matrix interpolation is a well-suited approach because…

For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov n-width describes the best-possible error for a reduced order model (ROM) of size n. In this paper, we provide approximation bounds for…

We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical…

This paper presents an H2-optimal model order reduction (MOR) method for linear systems with quadratic outputs based on Riemannian optimization. The H2-optimal MOR is formulated as an optimization problem in which the optimization variables…

Prediction+optimization is a common real-world paradigm where we have to predict problem parameters before solving the optimization problem. However, the criteria by which the prediction model is trained are often inconsistent with the goal…

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

In this paper we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems and variational inequalities. This framework allows to obtain many…

In nonlinear imaging problems whose forward model is described by a partial differential equation (PDE), the main computational bottleneck in solving the inverse problem is the need to solve many large-scale discretized PDEs at each step of…

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

In this work, we investigate a particular class of shape optimization problems under uncertainties on the input parameters. More precisely, we are interested in the minimization of the expectation of a quadratic objective in a situation…

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…

In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to…

Solving large-scale optimization on-the-fly is often a difficult task for real-time computer graphics applications. To tackle this challenge, model reduction is a well-adopted technique. Despite its usefulness, model reduction often…

High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…