Scientists are tackling the computational demands of modern particle physics with MadSpace, a novel phase-space and event-generation library. Theo Heimel, Olivier Mattelaer (both from CP3, Université catholique de Louvain), and Ramon Winterhalder (TIFLab, Università degli Studi di Milano & INFN Sezione di Milano) et al. have developed this C++ library with native support for GPUs via CUDA and HIP. MadSpace represents a significant advance by offering a unified, compute-graph-based framework for crucial processes including phase-space construction, adaptive and neural importance sampling, and event unweighting. Its modular design and capacity for end-to-end on-device workflows, coupled with a Python interface for libraries such as PyTorch, promise to accelerate simulations and facilitate the application of machine learning techniques to high-energy physics.
This C++ library, with native support for NVIDIA CUDA and AMD HIP, introduces a unified compute-graph framework designed to accelerate particle physics simulations. MadSpace addresses a critical bottleneck in high-energy physics by optimising phase-space construction, adaptive and neural importance sampling, and event unweighting, all while leveraging the power of modern GPUs.
The research team successfully integrated a wide range of mappings, extending from established techniques like the MadGraph multi-channel phase space to advanced, optimised normalizing flows featuring analytic inverse transformations. All components within MadSpace are designed to operate on batches of events, facilitating end-to-end workflows directly on the processing device.
This capability significantly reduces data transfer overhead and maximises computational efficiency. A high-level Python interface further enhances usability, enabling seamless integration with machine-learning libraries such as PyTorch. The development of MadSpace responds to the increasing demands of the High-Luminosity Large Hadron Collider, where theoretical simulations risk becoming a limiting factor in data analysis.
The core innovation lies in the library’s ability to efficiently generate first-principles theoretical predictions for particle collisions. By employing advanced sampling techniques and GPU acceleration, MadSpace aims to improve the speed, scalability, and modularity of these simulations. Researchers implemented high-performance versions of common Feynman-diagram-based mappings and novel Rambo-like schemes, including a GPU-tuned FastRambo variant.
Adaptive sampling routines, such as VEGAS and normalizing flows, are natively supported on GPUs, alongside a lightweight parton distribution interface. MadSpace’s modular design allows for easy integration with machine learning frameworks like MadNIS, opening avenues for efficient inference, surrogate modelling, and differentiable programming.
The upcoming major release of MadGraph will incorporate MadSpace as a core component, initially targeting leading-order computations with plans to extend functionality to next-to-leading order calculations. Beyond collider physics, the library’s architecture is designed to support machine learning-driven acceleration strategies and differentiable simulation frameworks, promising broader applications in scientific computing.
GPU Accelerated Phase-Space Generation and Event Simulation with MadSpace
MadSpace, a new modular phase-space and event-generation library, is constructed in C++ with native GPU support via CUDA and HIP. The library utilizes a unified compute-graph-based framework for phase-space construction, adaptive and neural importance sampling, and event unweighting, enabling end-to-end on-device workflows.
A high-level Python interface facilitates seamless integration with libraries such as PyTorch, broadening its applicability within machine learning contexts. The work addresses a gap in the MadGraph ecosystem by providing a fully featured and modular GPU-based phase-space generator. It implements common Feynman-diagram-based mappings and novel Rambo-like schemes, including a GPU-tuned FastRambo variant, to enhance computational efficiency.
Adaptive sampling routines, specifically VEGAS and normalizing flows, are natively supported on GPUs, alongside a lightweight parton distribution interface for comprehensive event simulation. At leading order, the evaluation of cross sections and event generation relies on the numerical computation of integrals over the phase space.
MadSpace employs Monte Carlo techniques, introducing an invertible mapping from a unit-hypercube to the physical phase space, denoted as G, to transform the integral into a more manageable form. This transformation utilizes the Jacobian determinant, g, to ensure normalized sampling density and efficient integration, approximating the target distribution as closely as possible.
To address the complexities of realistic collider applications, MadSpace incorporates multi-channel integration, decomposing the sampling density into complementary channels tailored to specific features of the integrand. The library supports both global and local multi-channeling strategies, offering flexibility in optimizing the variance of the integrand. Global multi-channeling combines individual channel densities with phase-space independent weights, while local multi-channeling utilizes phase-space dependent weights, allowing for a more nuanced approach to integration.
GPU accelerated phase-space generation with a stable mapping approximation
MadSpace, a new modular phase-space and event-generation library implemented in C++, offers native GPU support via CUDA and HIP. The framework utilizes a unified compute-graph-based approach for phase-space construction, adaptive and neural importance sampling, and event unweighting. This allows for end-to-end on-device workflows and seamless integration with libraries such as PyTorch.
The research details a numerically stable expression, r′ i (1 −bk) with bk = ck −(ck −2) r′ i, valid for all r′ i within the range of 0 to 1 and for any positive value of ck. This avoids computationally expensive numerical inversion steps during mapping approximations. Spline parameters, determined through a one-time fit minimizing the difference between the new mapping and the original RamboOnDiet mapping, are stored in a lookup table for efficient phase-space sampling.
The resulting values for k = 1 through 7 are detailed in Tab0.1. Implementation of the new mass measurement scheme significantly reduces computational cost.
High performance phase space generation using adaptive sampling and GPU acceleration
Scientists have developed MadSpace, a new library for constructing phase spaces and generating events in high-energy physics simulations. This C++ library utilizes modern hardware through native support for both CUDA and HIP, enabling computations on graphics processing units. MadSpace employs a unified compute-graph framework to facilitate efficient phase-space construction, adaptive and neural importance sampling, and event unweighting techniques.
The library incorporates a variety of mappings, ranging from conventional multi-channel phase spaces to more advanced normalizing flows with analytically invertible transformations. All components are designed to operate on batches of events, supporting complete on-device workflows and integrating seamlessly with frameworks like PyTorch via a high-level Python interface.
Validation studies confirm the accuracy of phase-space volumes and generated distributions, while performance benchmarks demonstrate substantial gains in event-generation throughput. The authors acknowledge limitations related to the complexity of fully exploiting the potential of massively parallel architectures and the ongoing need for optimization. Future research may focus on further enhancing the library’s capabilities and exploring its application to increasingly complex physics simulations, potentially addressing bottlenecks in the analysis pipelines of experiments like the High-Luminosity Large Hadron Collider.