Ultra-Ultra-Fast Flow Matching for On-the-Fly Event Generation

The Level-1 Scouting system introduced with the CMS Phase-2 upgrade captures reconstructed trigger objects at the full 40 MHz LHC collision rate. Stress-testing this system requires realistic input events sustained at this rate and delivered along the same path as real trigger data. Neither physics-based simulation nor generative models on external hardware can supply this. This work develops an on-the-fly generator of PUPPI kinematics that runs inside the Level-1 Trigger firmware itself, combining BDT-based flow matching with conifer's translation of BDTs into FPGA firmware. Generators are trained on minimum-bias data at two levels of granularity: whole jets, and the individual PUPPI particles constituting them. The jet-level velocity field and the numerical integrator were synthesised and built on the xcvu13p-flga2577-2-e chip of the Phase-2 Level-1 Trigger. The design occupies 20.4% of the device, achieves an initiation interval of one clock cycle at 360 MHz, and agrees bitwise with its HLS simulation. The on-chip generator sustains at least 22.5 million minimum-bias events per second, just over half the collision rate from a single instance, establishing that every stage of a flow-matching sampler can be expressed and run in trigger firmware. The sampler reproduces the bulk of each marginal and the broad shape of the pairwise densities. The limiting factor differs per channel: untuned fixed-point precision for $\eta$ and $\phi$, and the learnt field for $p_\mathrm{T}$, whose tail cuts off at 163 GeV. The constituent-level model raises the channel count from 3 to 49 and extrapolates to roughly 5.3 million LUTs, some three times the capacity of the chip; reducing this occupancy, for which BUFF's multi-output ensembles are the natural candidate, is the principal step remaining, though the multi-output model trained here does not yet reproduce the target. The implementation is released as puppibuff.