Related papers: Analysis-Aware Defeaturing of Dirichlet Features
This work presents a new approach to efficiently model the cathode in the moving boundary value problem of electrochemical machining. Until recently, the process simulation with finite elements had the drawback of remeshing required by the…
Deep neural networks often consist of a great number of trainable parameters for extracting powerful features from given datasets. On one hand, massive trainable parameters significantly enhance the performance of these deep networks. On…
We propose an algorithm for an optimal adaptive selection of points from the design domain of input random variables that are needed for an accurate estimation of failure probability and the determination of the boundary between safe and…
Border complexity captures functions that can be approximated by low-complexity ones. Debordering is the task of proving an upper bound on some non-border complexity measure in terms of a border complexity measure, thus getting rid of…
We present a novel, domain-agnostic, model-independent, unsupervised, and universally applicable Machine Learning approach for dimensionality reduction based on the principles of algorithmic complexity. Specifically, but without loss of…
The selection of features that are relevant for a prediction or classification problem is an important problem in many domains involving high-dimensional data. Selecting features helps fighting the curse of dimensionality, improving the…
A posteriori error estimates are an important tool to bound discretization errors in terms of computable quantities avoiding regularity conditions that are often difficult to establish. For non-linear and non-differentiable problems,…
Implicit sampling is a weighted sampling method that is used in data assimilation, where one sequentially updates estimates of the state of a stochastic model based on a stream of noisy or incomplete data. Here we describe how to use…
The 3D mesh is an important representation of geometric data. In the generation of mesh data, geometric deficiencies (e.g., duplicate elements, degenerate faces, isolated vertices, self-intersection, and inner faces) are unavoidable and may…
We introduce a boundary penalization technique to improve the spectral approximation of isogeometric analysis (IGA). The technique removes the outliers appearing in the high-frequency region of the approximate spectrum when using the…
In the present work, we derive functional upper bounds for the potential error arising from finite-element boundary-element coupling formulations for a nonlinear Poisson-type transmission problem. The proposed a posteriori error estimates…
Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…
Performance optimization of deep learning models is conducted either manually or through automatic architecture search, or a combination of both. On the other hand, their performance strongly depends on the target hardware and how…
Errors in biomechanics simulations arise from modeling and discretization. Modeling errors are due to the choice of the mathematical model whilst discretization errors measure the impact of the choice of the numerical method on the accuracy…
A shape optimization problem subject to an elliptic equation in the presence of missing data on the Dirichlet boundary condition is considered. It is formulated by optimizing the deformation field that varies the spatial domain where the…
We give a decomposition of the posterior predictive variance using the law of total variance and conditioning on a finite dimensional discrete random variable. This random variable summarizes various features of modeling that are used to…
Recently, the enactment of privacy regulations has promoted the rise of the machine unlearning paradigm. Existing studies of machine unlearning mainly focus on sample-wise unlearning, such that a learnt model will not expose user's privacy…
We present a method of CutFEM type for the Poisson problem with either Dirichlet or Neumann boundary conditions. The computational mesh is obtained from a background (typically uniform Cartesian) mesh by retaining only the elements…
Traditional evaluation metrics for learned models that report aggregate scores over a test set are insufficient for surfacing important and informative patterns of failure over features and instances. We introduce and study a method aimed…
We propose a novel a posteriori error estimator for conforming finite element discretizations of two- and three-dimensional Helmholtz problems. The estimator is based on an equilibrated flux that is computed by solving patchwise mixed…