Related papers: Convolution tensor decomposition for efficient hig…
The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…
For many inverse parameter problems for partial differential equations in which the domain contains only well-separated objects, an asymptotic solution to the forward problem involving 'polarization tensors' exists. These are functions of…
This paper addresses the problem of finding interpretable directions in the latent space of pre-trained Generative Adversarial Networks (GANs) to facilitate controllable image synthesis. Such interpretable directions correspond to…
In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal semi-discretization scheme and a space-time full-discretization scheme were, respectively, introduced and analyzed for the additive noise-driven stochastic…
In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…
One of the main issues in computing a tensor decomposition is how to choose the number of rank-one components, since there is no finite algorithms for determining the rank of a tensor. A commonly used approach for this purpose is to find a…
Tensor decomposition plays a key role in identifying common features across a collection of matrices in many areas of science. A fundamental need in big data research is to process data tabulated as large-scale matrices using eigenvectors.…
We present a phase field modeling framework for hydrogen assisted cracking. The model builds upon a coupled mechanical and hydrogen diffusion response, driven by chemical potential gradients, and a hydrogen-dependent fracture energy…
Allen--Cahn equation with constant and degenerate mobility, and with polynomial and logarithmic energy functionals is discretized using symmetric interior penalty discontinuous Galerkin (SIPG) finite elements in space. We show that the…
Explicit step-truncation tensor methods have recently proven successful in integrating initial value problems for high-dimensional partial differential equations (PDEs). However, the combination of non-linearity and stiffness may introduce…
This paper introduces a new boundary element formulation for transient electromagnetic scattering by homogeneous dielectric objects based on the time-domain PMCHWT equation. To address dense-mesh breakdown, a multiplicative Calderon…
Magnetic resonance (MR)-$T_2^*$ mapping is widely used to study hemorrhage, calcification and iron deposition in various clinical applications, it provides a direct and precise mapping of desired contrast in the tissue. However, the long…
In this paper, we present a comprehensive study and propose several novel techniques for implementing 3D convolutional blocks using 2D and/or 1D convolutions with only 4D and/or 3D tensors. Our motivation is that 3D convolutions with 5D…
For the arbitrary-Lagrangian-Eulerian (ALE) calculations, the geometric information needs to be calculated at each time step due to the movement of mesh. To achieve the high-order spatial accuracy, a large number of matrix inversions are…
We propose an efficient end-to-end deep learning method for solving nonlocal Allen-Cahn (AC) and Cahn-Hilliard (CH) phase-field models. One motivation for this effort emanates from the fact that discretized partial differential…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
We investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
In this paper, the mathematical properties and numerical discretizations of multiphase models that simulate the phase separation of an $N$-component mixture are studied. For the general choice of phase variables, the unisolvent property of…
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems…