Related papers: Eigenvalue Mapping-based Discretization of the Gen…
The gradient discretisation method is a generic framework that is applicable to a number of schemes for diffusion equations, and provides in particular generic error estimates in $L^2$ and $H^1$-like norms. In this paper, we establish an…
The randomized midpoint method, proposed by [SL19], has emerged as an optimal discretization procedure for simulating the continuous time Langevin diffusions. Focusing on the case of strong-convex and smooth potentials, in this paper, we…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
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…
Hyperspectral analysis has gained popularity over recent years as a way to infer what materials are displayed on a picture whose pixels consist of a mixture of spectral signatures. Computing both signatures and mixture coefficients is known…
The dynamic matrix method addresses the Landau-Lifshitz-Gilbert (LLG) equation in the frequency domain by transforming it into an eigenproblem. Subsequent numerical solutions are derived from the eigenvalues and eigenvectors of the dynamic…
The deep learning recipe of casting real-world problems as mathematical optimisation and tackling the optimisation by training deep neural networks using gradient-based optimisation has undoubtedly proven to be a fruitful one. The…
In the present work, advanced spatial and temporal discretization techniques are tailored to hyperelastic physics-augmented neural networks, i.e., neural network based constitutive models which fulfill all relevant mechanical conditions of…
Matrix factorization (MF) mechanisms for differential privacy (DP) have substantially improved the state-of-the-art in privacy-utility-computation tradeoffs for ML applications in a variety of scenarios, but in both the centralized and…
We propose a differentially private data generation paradigm using random feature representations of kernel mean embeddings when comparing the distribution of true data with that of synthetic data. We exploit the random feature…
Recent research in nonlinear filtering and signal processing has suggested an efficient derivative-free Extended Kalman filter (EKF) designed for discrete-time stochastic systems. Such approach, however, has failed to address the estimation…
Regularisation allows one to handle ill-posed inverse problems. Here we focus on discrete unfolding problems. The properties of the results are characterised by the consistency between measurements and unfolding result and by the posterior…
Recently, deep matrix factorization has been established as a powerful model for unsupervised tasks, achieving promising results, especially for multi-view clustering. However, existing methods often lack effective feature selection…
The shuffle model of local differential privacy is an advanced method of privacy amplification designed to enhance privacy protection with high utility. It achieves this by randomly shuffling sensitive data, making linking individual data…
From characterizing the speed of a thermal system's response to computing natural modes of vibration, eigenvalue analysis is ubiquitous in engineering. In spite of this, eigenvalue problems have received relatively little treatment compared…
Feature selection with specific multivariate performance measures is the key to the success of many applications, such as image retrieval and text classification. The existing feature selection methods are usually designed for…
In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…
Online parameter controllers for evolutionary algorithms adjust values of parameters during the run of an evolutionary algorithm. Recently a new efficient parameter controller based on reinforcement learning was proposed by Karafotias et…
Finite difference discretization schemes preserving a subgroup of the maximal Lie invariance group of the one-dimensional linear heat equation are determined. These invariant schemes are constructed using the invariantization procedure for…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…