Related papers: Grid-based lattice summation of electrostatic pote…
We consider the approximate recovery of multivariate periodic functions from a discrete set of function values taken on a rank-$s$ integration lattice. The main result is the fact that any (non-)linear reconstruction algorithm taking…
We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…
The large sparse linear systems arising from the finite element or finite difference discretization of elliptic PDEs can be solved directly via, e.g., nested dissection or multifrontal methods. Such techniques reorder the nodes in the grid…
Tensor network contraction is central to problems ranging from many-body physics to computer science. We describe how to approximate tensor network contraction through bond compression on arbitrary graphs. In particular, we introduce a…
We present efficient, sketching-based methods for the summation of tensors in Tucker format. Leveraging the algebraic structure of Khatri-Rao and Kronecker products, our approach enables compressed arithmetic on Tucker tensors while…
The Vlasov-Maxwell equations provide an \textit{ab-initio} description of collisionless plasmas, but solving them is often impractical because of the wide range of spatial and temporal scales that must be resolved and the high…
Firms earning prediction plays a vital role in investment decisions, dividends expectation, and share price. It often involves multiple tensor-compatible datasets with non-linear multi-way relationships, spatiotemporal structures, and…
We present a new approach to efficiently simulate electrolytes confined between infinite charged walls using a 3d Ewald summation method. The optimal performance is achieved by separating the electrostatic potential produced by the charged…
We present a unified framework to describe lattice gauge theories by means of tensor networks: this framework is efficient as it exploits the high amount of local symmetry content native of these systems describing only the gauge invariant…
This study aims to solve the over-reliance on the rank estimation strategy in the standard tensor factorization-based tensor recovery and the problem of a large computational cost in the standard t-SVD-based tensor recovery. To this end, we…
Quantum and tensor network simulations have emerged as prominent sign-problem free approaches to lattice gauge theories. Unlike conventional Markov chain Monte Carlo methods, they are based on the Hamiltonian formulation. In this talk, we…
The development of tensor renormalization group (TRG) algorithm in higher dimensions is an important and urgent task, as the TRG is expected to provide a way to overcome the sign problem in lattice quantum chromodynamics (QCD) calculations…
By definition, a rigid graph in $\mathbb{R}^d$ (or on a sphere) has a finite number of embeddings up to rigid motions for a given set of edge length constraints. These embeddings are related to the real solutions of an algebraic system.…
We propose a generalized Lanczos method to generate the many-body basis states of quantum lattice models using tensor-network states (TNS). The ground-state wave function is represented as a linear superposition composed from a set of TNS…
We present a fast summation method for lattice sums of the type which arise when solving wave scattering problems with periodic boundary conditions. While there are a variety of effective algorithms in the literature for such calculations,…
Combining sum factorization, weighted quadrature, and row-based assembly enables efficient higher-order computations for tensor product splines. We aim to transfer these concepts to immersed boundary methods, which perform simulations on a…
We propose a new representation for encoding 3D shapes as neural fields. The representation is designed to be compatible with the transformer architecture and to benefit both shape reconstruction and shape generation. Existing works on…
We present full accounts of a method to extract nucleon-nucleon (NN) potentials from the Bethe-Salpter amplitude in lattice QCD. The method is applied to two nucleons on the lattice with quenched QCD simulations. By disentangling the mixing…
Matrices are exceptionally useful in various fields of study as they provide a convenient framework to organize and manipulate data in a structured manner. However, modern matrices can involve billions of elements, making their storage and…
We analyze combinatorial structures which play a central role in determining spectral properties of the volume operator in loop quantum gravity (LQG). These structures encode geometrical information of the embedding of arbitrary valence…