FPGA Acceleration of Matrix-Element Calculations for Monte Carlo Event Generation
We present an FPGA-based study of matrix-element acceleration for Monte Carlo event generation, using MadGraph5_aMC@NLO as a benchmark framework. Two complementary scenarios are considered. First, we implement the full matrix-element workflow on an AMD Alveo U250 accelerator for the benchmark process $e^+e^- \to \mu^+\mu^-$, enabling an end-to-end evaluation of FPGA acceleration for a simple process. Second, for the more complex $gg \to t\bar{t}+X$ processes with increasing jet multiplicity, we investigate FPGA acceleration of the color-algebra kernels as a structured and scalable entry point for selective acceleration. In this second case, the reported speedups correspond to the isolated color-reduction kernel operating on precomputed amplitudes, rather than to the full matrix-element evaluation or the complete event-generation workflow. The proposed implementations are developed using High-Level Synthesis and are evaluated in terms of numerical accuracy, performance, energy efficiency, resource utilization, and scalability. Compared with CPU and GPU implementations available within the MG5aMC framework, the FPGA solutions achieve substantial speedups and significantly improved energy efficiency. For the considered benchmarks, the numerical results remain in close agreement with the corresponding CPU reference calculations, while the resource analysis highlights the importance of numerical representation in determining scalability on FPGA devices. These results support the use of FPGAs as a competitive architecture for selected Monte Carlo event-generation workloads in high-energy physics.