Related papers: Efficient Numerical Integration for Finite Element…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
Matrix and tensor completion aim to recover a low-rank matrix / tensor from limited observations and have been commonly used in applications such as recommender systems and multi-relational data mining. A state-of-the-art matrix completion…
Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
In this paper, a mechanistic data-driven approach is proposed to accelerate structural topology optimization, employing an in-house developed finite element convolutional neural network (FE-CNN). Our approach can be divided into two stages:…
This paper is concerned with achieving optimal coherence for highly redundant real unit-norm frames. As the redundancy grows, the number of vectors in the frame becomes too large to admit equiangular arrangements. In this case, other…
We present a new rank-adaptive tensor method to compute the numerical solution of high-dimensional nonlinear PDEs. The method combines functional tensor train (FTT) series expansions, operator splitting time integration, and a new…
Polynomial approximations of functions are widely used in scientific computing. In certain applications, it is often desired to require the polynomial approximation to be non-negative (resp. non-positive), or bounded within a given range,…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we…
Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order of interpolation for the displacement and phase-field variables. Most common is to use linear…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
In this study, we introduce a novel family of tensor networks, termed constrained matrix product states (MPS), designed to incorporate exactly arbitrary discrete linear constraints, including inequalities, into sparse block structures.…
The task of finding the optimal compression of a polyline with straight-line segments and arcs is performed in many applications, such as polyline compression, noise filtering, and feature recognition. Optimal compression algorithms find…
Dense 3D convolutions provide high accuracy for perception but are too computationally expensive for real-time robotic systems. Existing tri-plane methods rely on 2D image features with interpolation, point-wise queries, and implicit MLPs,…
Finite element methods for electromagnetic problems modeled by Maxwell-type equations are highly sensitive to the conformity of approximation spaces, and non-conforming methods may cause loss of convergence. This fact leads to an essential…
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…
We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by…