Related papers: Semantic 3D Reconstruction with Finite Element Bas…

In this paper, we propose a deep-learning-based approach to a class of multiscale problems. THe Generalized Multiscale Finite Element Method (GMsFEM) has been proven successful as a model reduction technique of flow problems in…

Given labeled points in a high-dimensional vector space, we seek a low-dimensional subspace such that projecting onto this subspace maintains some prescribed distance between points of differing labels. Intended applications include…

Many problems in science and engineering can be rigorously recast into minimizing a suitable energy functional. We have been developing efficient and flexible solution strategies to tackle various minimization problems by employing finite…

Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…

Deep neural networks suffer from catastrophic forgetting, where performance on previous tasks degrades after training on a new task. This issue arises due to the model's tendency to overwrite previously acquired knowledge with new…

Few-shot image classification requires the classifier to robustly cope with unseen classes even if there are only a few samples for each class. Recent advances benefit from the meta-learning process where episodic tasks are formed to train…

A widely used algorithm for transfer learning is fine-tuning, where a pre-trained model is fine-tuned on a target task with a small amount of labeled data. When the capacity of the pre-trained model is significantly larger than the size of…

Weakly supervised semantic segmentation aims to achieve pixel-level predictions using image-level labels. Existing methods typically entangle semantic recognition and object localization, which often leads models to focus exclusively on…

Recovered finite element methods (R-FEM) have been recently introduced for meshes consisting of simplicial and/or box-type meshes. Here, utilising the flexibility of R-FEM framework, we extend their definition on polygonal and polyhedral…

Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and…

A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…

The strength of machine learning models stems from their ability to learn complex function approximations from data; however, this strength also makes training deep neural networks challenging. Notably, the complex models tend to memorize…

We present a new discretization method for homogeneous convection-diffusion-reaction boundary value problems in 3D that is a non-standard finite element method with PDE-harmonic shape functions on polyhedral elements. The element stiffness…

This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…

Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that…

This paper generalizes the non-conforming FEM of Crouzeix and Raviart and its fundamental projection property by a novel mixed formulation for the Poisson problem based on the Helmholtz decomposition. The new formulation allows for ansatz…

This paper concerns pseudo labelling in segmentation. Our contribution is fourfold. Firstly, we present a new formulation of pseudo-labelling as an Expectation-Maximization (EM) algorithm for clear statistical interpretation. Secondly, we…

In the discretization of differential problems on complex geometrical domains, discretization methods based on polygonal and polyhedral elements are powerful tools. Adaptive mesh refinement for such kind of problems is very useful as well…

With the introduction of fully convolutional neural networks, deep learning has raised the benchmark for medical image segmentation on both speed and accuracy, and different networks have been proposed for 2D and 3D segmentation with…

This work presents a reduced order modelling technique built on a high fidelity embedded mesh finite element method. Such methods, and in particular the CutFEM method, are attractive in the generation of projection-based reduced order…