Nanosecond hardware regression trees in FPGA at the LHC

Abstract

We present a generic parallel implementation of the decision tree-based machine learning (ML) method in hardware description language (HDL) on field programmable gate arrays (FPGA). A regression problem in high energy physics at the Large Hadron Collider is considered: the estimation of the magnitude of missing transverse momentum using boosted decision trees (BDT). A forest of twenty decision trees each with a maximum depth of ten using eight input variables of 16-bit precision is executed with a latency of less than 10 ns using O(0.1%) resources on Xilinx UltraScale+ VU9P -- approximately ten times faster and five times smaller compared to similar designs using high level synthesis (HLS) -- without the use of digital signal processors (DSP) while eliminating the use of block RAM (BRAM). We also demonstrate a potential application in the estimation of muon momentum for ATLAS RPC at HL-LHC.