相关论文: An NPDo Approach for Tensor Block-Diagonalization

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…

This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…

Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…

A numerical method is proposed to solve the full-Eulerian time-dependent Vlasov-Poisson system in high dimension. The algorithm relies on the construction of a tensor decomposition of the solution whose rank is adapted at each time step.…

Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

The Tucker tensor decomposition is a natural extension of the singular value decomposition (SVD) to multiway data. We propose to accelerate Tucker tensor decomposition algorithms by using randomization and parallelization. We present two…

The Transverse Momentum Dependent (TMD) Parton Branching (PB) method incorporates elements of TMD physics into a Monte Carlo (MC) framework to produce high-energy QCD predictions for collider processes. It derives TMDs from the PB evolution…

When the amount of entanglement in a quantum system is limited, the relevant dynamics of the system is restricted to a very small part of the state space. When restricted to this subspace the description of the system becomes efficient in…

Nonsmooth composite optimization with orthogonality constraints has a wide range of applications in statistical learning and data science. However, this problem is challenging due to its nonsmooth objective and computationally expensive…

This paper addresses the challenge of reconstructing a 3D power spectrum map from sparse, scattered, and incomplete spectrum measurements. It proposes an integrated approach combining interpolation and block-term tensor decomposition (BTD).…

Partial Differential Equations (PDEs) are used to model a variety of dynamical systems in science and engineering. Recent advances in deep learning have enabled us to solve them in a higher dimension by addressing the curse of…

Symmetric tensor operations arise in a wide variety of computations. However, the benefits of exploiting symmetry in order to reduce storage and computation is in conflict with a desire to simplify memory access patterns. In this paper, we…

We present a new class of efficient and robust discontinuous spectral-element methods of arbitrary order for nonlinear hyperbolic systems of conservation laws on curved triangular and tetrahedral unstructured grids. Such discretizations…

Fast computation of singular value decomposition (SVD) is of great interest in various machine learning tasks. Recently, SVD methods based on randomized linear algebra have shown significant speedup in this regime. This paper attempts to…

Numerous complex real-world systems, such as those in biological, ecological, and social networks, exhibit higher-order interactions that are often modeled using polynomial dynamical systems or homogeneous polynomial dynamical systems…

Wall-clock-time is minimized for a solution to a linear-program with block-diagonal-structure, by decomposing the linear-program into as many small-sized subproblems as possible, each block resulting in a separate subproblem, when the…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

Tensor computation has emerged as a powerful mathematical tool for solving high-dimensional and/or extreme-scale problems in science and engineering. The last decade has witnessed tremendous advancement of tensor computation and its…

The Parton Branching (PB) Method describes the evolution of transverse momentum dependent parton densities (TMDs). The obtained TMDs can be used in Monte Carlo generators to describe physical observables. We give an overview of recent…