Related papers: Adaptive $h$-refinement for reduced-order models
An adaptive parametric reduced-order modeling method based on interpolating poles of reduced-order models is proposed in this paper. To guarantee correct interpolation, a pole-matching process is conducted to determine which poles of two…
An adaptive projection-based reduced-order model (ROM) formulation is presented for model-order reduction of problems featuring chaotic and convection-dominant physics. An efficient method is formulated to adapt the basis at every time-step…
This paper presents a reduced-order approach for four-dimensional variational data assimilation, based on a prior EO F analysis of a model trajectory. This method implies two main advantages: a natural model-based definition of a mul…
In this paper, we present two adaptive methods for the basis enrichment of the mixed Generalized Multiscale Finite Element Method (GMsFEM) for solving the flow problem in heterogeneous media. We develop an a-posteriori error indicator which…
This contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and…
The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…
In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear…
We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…
In this contribution we present a survey of concepts in localized model order reduction methods for parameterized partial differential equations. The key concept of localized model order reduction is to construct local reduced spaces that…
We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…
We propose a new problem formulation and a corresponding evaluation framework to advance research on unsupervised domain adaptation for semantic image segmentation. The overall goal is fostering the development of adaptive learning systems…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
Deep learning-based models have demonstrated remarkable success in solving illposed inverse problems; however, many fail to strictly adhere to the physical constraints imposed by the measurement process. In this work, we introduce a…
In this paper we generalize to non-uniform grids of quad-tree type the Compact WENO reconstruction of Levy, Puppo and Russo (SIAM J. Sci. Comput., 2001), thus obtaining a truly two-dimensional non-oscillatory third order reconstruction with…
We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…
Distributed model fitting refers to the process of fitting a mathematical or statistical model to the data using distributed computing resources, such that computing tasks are divided among multiple interconnected computers or nodes, often…
We consider the problem of planning views for a robot to acquire images of an object for visual inspection and reconstruction. In contrast to offline methods which require a 3D model of the object as input or online methods which rely on…
In the recent years, the desire and need to understand sequential data has been increasing, with particular interest in sequential contexts such as patient monitoring, understanding daily activities, video surveillance, stock market and the…
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…
A general method for accelerating fixed point schemes for problems related to partial differential equations is presented in this article. The speedup is obtained by training a reduced-order model on-the-fly, removing the need to do an…