Related papers: Efficient Numerical Integration for Finite Element…

For nonlinear reduced-order models, especially for those with non-polynomial nonlinearities, the computational complexity still depends on the dimension of the original dynamical system. As a result, the reduced-order model loses its…

We introduce tensor numerical techniques for solving optimal control problems constrained by elliptic operators in $\mathbb{R}^d$, $d=2,3$, with variable coefficients, which can be represented in a low rank separable form. We construct a…

Numerical integration is a foundational technique in scientific computing and is at the core of many computer vision applications. Among these applications, neural volume rendering has recently been proposed as a new paradigm for view…

Metric embedding has become a common technique in the design of algorithms. Its applicability is often dependent on how high the embedding's distortion is. For example, embedding finite metric space into trees may require linear distortion…

Polynomial optimization problems are infinite-dimensional, nonconvex, NP-hard, and are often handled in practice with the moment-sums of squares hierarchy of semidefinite programming bounds. We consider problems where the objective function…

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…

Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…

In this paper, we study first-order methods on a large variety of low-rank matrix optimization problems, whose solutions only live in a low dimensional eigenspace. Traditional first-order methods depend on the eigenvalue decomposition at…

Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent generating complex 3D interface-fitted meshes. However, many…

Despite extensive research on symmetric polynomial quadrature rules for triangles, as well as approaches to their calculation, few studies have focused on non-polynomial functions, particularly on their integration using symmetric triangle…

Due to the limit of mesh density, the improvement of the spatial precision of numerical computation always leads to a decrease in computing efficiency. Aiming at this inability of numerical computation, we propose a novel method for…

We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

We present a novel method for reconstructing parametric, volumetric, multi-story building models from unstructured, unfiltered indoor point clouds by means of solving an integer linear optimization problem. Our approach overcomes…

Learning embedding table plays a fundamental role in Click-through rate(CTR) prediction from the view of the model performance and memory usage. The embedding table is a two-dimensional tensor, with its axes indicating the number of feature…

Accurate simulations of various physical processes on digital computers requires huge computing performance, therefore accelerating these scientific and engineering applications has a great importance. Density of programmable logic devices…

Computing an optimal classification tree that provably maximizes training performance within a given size limit, is NP-hard, and in practice, most state-of-the-art methods do not scale beyond computing optimal trees of depth three.…

Approximation of non-linear kernels using random feature maps has become a powerful technique for scaling kernel methods to large datasets. We propose $\textit{Tensor Sketch}$, an efficient random feature map for approximating polynomial…

We consider convex optimization problems formulated using dynamic programming equations. Such problems can be solved using the Dual Dynamic Programming algorithm combined with the Level 1 cut selection strategy or the Territory algorithm to…

In this paper, we propose a scalable approximate multiplier design, scaleTRIM, that approximates the multiplication operation using fitted linear functions, also referred to as linearization. We show that multiplication operations can be…