相关论文: GPU Implementation of Zippel Method for Feynman In…

We present a new algorithm for integration-by-parts (IBP) reduction of Feynman integrals with high powers of numerators or propagators, a demanding computational step in evaluating multi-loop scattering amplitudes. The algorithm allows us…

In generalized graph signal processing (GGSP), the signal associated with each vertex in a graph is an element from a Hilbert space. In this paper, we study GGSP signal reconstruction as a kernel ridge regression (KRR) problem. By devising…

The phase-integral method (PIM) is an asymptotic method of the geometrical optics or semi-classical type for solving approximately, but in many cases very accurately, a wide class of differential equations in physics. Unlike the related…

The fast multipole method (FMM) has received growing attention in the beam physics simulation. In this study, we formulate an interpolation-based FMM for the computation of the relativistic space-charge field. Different to the…

We report on an implementation within GiNaC to evaluate iterated integrals related to elliptic Feynman integrals numerically to arbitrary precision within the region of convergence of the series expansion of the integrand. The…

In this work, we evaluate the use of superpixel pooling layers in deep network architectures for semantic segmentation. Superpixel pooling is a flexible and efficient replacement for other pooling strategies that incorporates spatial prior…

A novel and detailed convergence analysis is presented for a greedy algorithm that was previously introduced for operator reconstruction problems in the field of quantum mechanics. This algorithm is based on an offline/online decomposition…

Bilevel optimization enjoys a wide range of applications in emerging machine learning and signal processing problems such as hyper-parameter optimization, image reconstruction, meta-learning, adversarial training, and reinforcement…

The generalized eigenvalue problem (GEP) serves as a cornerstone in a wide range of applications in numerical linear algebra and scientific computing. However, traditional approaches that aim to maximize the classical Rayleigh quotient…

We describe a version of the FGLM algorithm that can be used to compute generic fibers of positive-dimensional polynomial ideals. It combines the FGLM algorithm with a Hensel lifting strategy. In analogy with Hensel lifting, we show that…

Processing large-scale graph datasets is computationally intensive and time-consuming. Processor-centric CPU and GPU architectures, commonly used for graph applications, often face bottlenecks caused by extensive data movement between the…

The rapid growth in machine learning models, especially in natural language processing and computer vision, has led to challenges when running these models on hardware with limited resources. This paper introduces Superpipeline, a new…

This work is concerned with the kernel-based approximation of a complex-valued function from data, where the frequency response function of a partial differential equation in the frequency domain is of particular interest. In this setting,…

Integration-by-parts reductions play a central role in perturbative QFT calculations. They allow the set of Feynman integrals contributing to a given observable to be reduced to a small set of basis integrals, and they moreover facilitate…

Present and future high-precision tests of the Standard Model and beyond for the fundamental constituents and interactions in Nature are demanding complex perturbative calculations involving multi-leg and multi-loop Feynman diagrams.…

Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…

This paper explores practical aspects of using a high-level functional language for GPU-based arithmetic on ``midsize'' integers. By this we mean integers of up to about a quarter million bits, which is sufficient for most practical…

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear…

We present a set of rules to guide the design of GPU algorithms. These rules are grounded on the principle of reducing waste in GPU utility to achieve good speed up. In accordance to these rules, we propose GPU algorithms for 2D…

In the Lee-Pomeransky representation, Feynman integrals can be identified as a subset of Euler-Mellin integrals, which are known to satisfy Gel'fand-Kapranov-Zelevinsky (GKZ) system of partial differential equations. Here we present an…