相关论文: ftint: Calculating gradient-flow integrals with py…

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical…

This paper presents a novel approach for numerical solution of a class of fourth order time fractional partial differential equations (PDE's). The finite difference formulation has been used for temporal discretization, whereas, the space…

We present the program SecDec 2.0 which contains various new features: First, it allows the numerical evaluation of multi-loop integrals with no restriction on the kinematics. Dimensionally regulated ultraviolet and infrared singularities…

We present the first numerical investigation of the method proposed in Ref. [1] to utilize gradient flow to obtain precise determinations of higher moments of PDFs from lattice QCD, circumventing power divergent mixing with lower…

Integer-valued elements of an integral submodular flow polyhedron $Q$ are investigated which are decreasingly minimal (dec-min) in the sense that their largest component is as small as possible, within this, the second largest component is…

We study a recently-proposed approach to the numerical evaluation of multi-loop Feynman integrals using available sector decomposition programs. As our main example, we consider the two-loop integrals for the $\alpha \alpha_s$ corrections…

The technique coined as NDIM - Negative Dimensional Integration Method by their discoverers, relies on a three-pronged basis: Gaussian integration, series expansion and analytic continuation. The technique has been successfully applied to…

Negative dimensional integration method (NDIM) is a technique to deal with D-dimensional Feynman loop integrals. Since most of the physical quantities in perturbative Quantum Field Theory (pQFT) require the ability of solving them, the…

We use a space-time discretization based on physics informed deep learning (PIDL) to approximate solutions of a class of rate-dependent strain gradient plasticity models. The differential equation governing the plastic flow, the so-called…

This article presents a new high-order accurate algorithm for finding a particular solution to a linear, constant-coefficient partial differential equation (PDE) by means of a convolution of the volumetric source function with the Green's…

A nonlinear parabolic equation of sixth order is analyzed. The equation arises as a reduction of a model from quantum statistical mechanics, and also as the gradient flow of a second-order information functional with respect to the…

Many physical, biological or chemical systems are modeled by ordinary differential equations (ODEs) and finding their solution is an every-day-task for many scientists. Here, we introduce a new C++ library dedicated to find numerical…

SecDec is a program which can be used for the evaluation of parametric integrals, in particular multi-loop integrals. For a given set of propagators defining the graph, the program constructs the graph polynomials, factorizes the endpoint…

Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore,…

We construct a kinetic model for matter-radiation interactions whose hydrodynamic gradient expansion can be computed analytically up to infinite order in derivatives, in the fully nonlinear regime, and for arbitrary flows. The frequency…

Scientific simulations and experimental measurements produce vast amounts of spatio-temporal data, yet extracting meaningful insights remains challenging due to high dimensionality, complex structures, and missing information. Traditional…

The solutions to many problems in the mathematical, computational, and physical sciences often involve multidimensional integrals. A direct numerical evaluation of the integral incurs a computational cost that is exponential in the number…

Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector…

In many computational problems in engineering and science, function or model differentiation is essential, but also integration is needed. An important class of computational problems include so-called integro-differential equations which…

We present updates on the development of pySecDec, a toolbox to numerically evaluate parameter integrals in the context of dimensional regularization. We discuss difficulties with loop integrals in the special kinematic condition where the…