Related papers: Optimal morphings for model-order reduction for po…

Morphological neural networks, or layers, can be a powerful tool to boost the progress in mathematical morphology, either on theoretical aspects such as the representation of complete lattice operators, or in the development of image…

In this paper, we consider the problem of partitioning a polygon into a set of connected disjoint sub-polygons, each of which covers an area of a specific size. The work is motivated by terrain covering applications in robotics, where the…

Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…

This paper deals with model-order reduction of parametric partial differential equations (PPDE). More specifically, we consider the problem of finding a good approximation subspace of the solution manifold of the PPDE when only partial…

We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution…

We consider an optimization problem related to semi-active damping of vibrating systems. The main problem is to determine the best damping matrix able to minimize influence of the input on the output of the system. We use a minimization…

We develop a new optimisation technique that combines multiresolution subdivision surfaces for boundary description with immersed finite elements for the discretisation of the primal and adjoint problems of optimisation. Similar to wavelets…

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 paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…

In order to solve partial differential equations numerically and accurately, a high order spatial discretization is usually needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretized systems…

Submodular function minimization is a fundamental optimization problem that arises in several applications in machine learning and computer vision. The problem is known to be solvable in polynomial time, but general purpose algorithms have…

This paper describes the use of a quadratic manifold for the model order reduction of structural dynamics problems featuring geometric nonlinearities. The manifold is tangent to a subspace spanned by the most relevant vibration modes, and…

A model-order reduction framework for the meshless smoothed-particle hydrodynamics (SPH) method is presented. The proposed framework introduces the concept of modal reference spaces to overcome the challenges of discovering low-dimensional…

In this paper, we introduce a higher-order multiscale method for time-dependent problems with highly oscillatory coefficients. Building on the localized orthogonal decomposition (LOD) framework, we construct enriched correction operators to…

In this work, we consider methods for solving large-scale optimization problems with a possibly nonsmooth objective function. The key idea is to first specify a class of optimization algorithms using a generic iterative scheme involving…

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is…

In shape optimisation it is desirable to obtain deformations of a given mesh without negative impact on the mesh quality. We propose a new algorithm using least square formulations of the Cauchy-Riemann equations. Our method allows to…

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…

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…

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks…