Vegas Revisited: Adaptive Monte Carlo Integration Beyond Factorization

We describe a new algorithm, VEGAS+, for adaptive multidimensional Monte Carlo integration. The new algorithm adds a second adaptive strategy, adaptive stratified sampling, to the adaptive importance sampling that is the basis for its widely used predecessor VEGAS. Both VEGAS and VEGAS+ are effective for integrands with large peaks, but VEGAS+ can be much more effective for integrands with multiple peaks or other significant structures aligned with diagonals of the integratio...

This paper shortly describes some important changes to the pvegas-code since its first publication. It proceeds with a report on the scaling-behavior that was found on a wide range of current parallel hardware and discusses some issues of optimization that may be thrown up.

This paper introduces cuVegas, a CUDA-based implementation of the Vegas Enhanced Algorithm (VEGAS+), optimized for multi-dimensional integration in GPU environments. The VEGAS+ algorithm is an advanced form of Monte Carlo integration, recognized for its adaptability and effectiveness in handling complex, high-dimensional integrands. It employs a combination of variance reduction techniques, namely adaptive importance sampling and a variant of adaptive stratified sampling, tha...

We present VegasFlow, a new software for fast evaluation of high dimensional integrals based on Monte Carlo integration techniques designed for platforms with hardware accelerators. The growing complexity of calculations and simulations in many areas of science have been accompanied by advances in the computational tools which have helped their developments. VegasFlow enables developers to delegate all complicated aspects of hardware or platform implementation to the library ...

Monte Carlo (MC) integration is an important calculational technique in the physical sciences. Practical considerations require that the calculations are performed as accurately as possible for a given set of computational resources. To improve the accuracy of MC integration, a number of useful variance reduction algorithms have been developed, including importance sampling and control variates. In this work, we demonstrate how these two methods can be applied simultaneously,...

We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion and are runtime and memory optimised, respectively. SINGINT, a C implementation of the algorithms, is introduced and its utilisation in the calculation of particle scattering amplitudes is exemplified.

We consider several issues related to the multidimensional integration using a network of heterogeneous computers. Based on these considerations, we develop a new general purpose scheme which can significantly reduce the time needed for evaluation of integrals with CPU intensive integrands. This scheme is a parallel version of the well-known adaptive Monte Carlo method (the VEGAS algorithm), and is incorporated into a new integration package which uses the standard set of mes...

A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is performed with emphasis on certain features of a theoretical prediction. Adaptive integration algorithms are well-suited to perform this task very efficiently. Predictions which depend on parameter spaces with many dimensions call for such an adapt...

In this work we demonstrate the usage of the VegasFlow library on multidevice situations: multi-GPU in one single node and multi-node in a cluster. VegasFlow is a new software for fast evaluation of highly parallelizable integrals based on Monte Carlo integration. It is inspired by the Vegas algorithm, very often used as the driver of cross section integrations and based on Google's powerful TensorFlow library. In this proceedings we consider a typical multi-GPU configuration...

Monte Carlo (MC) methods for numerical integration seem to be embarassingly parallel on first sight. When adaptive schemes are applied in order to enhance convergence however, the seemingly most natural way of replicating the whole job on each processor can potentially ruin the adaptive behaviour. Using the popular VEGAS-Algorithm as an example an economic method of semi-micro parallelization with variable grain-size is presented and contrasted with another straightforward ap...