APEX-KF: Physics-Aware Adaptive Precision Kalman Filtering for GPU-Accelerated Particle Track Reconstruction

The High-Luminosity Large Hadron Collider (HL-LHC) will increase event pile-up to the point where charged-particle track reconstruction dominates the offline computing budget, motivating both accelerator offload and reduced numerical precision. Uniform half-precision (FP16) tracking is attractive for throughput but degrades the momentum estimate of stiff, high-transverse-momentum (pT) tracks, whose small sagitta is most sensitive to coordinate rounding. This work presents APEX-KF (Adaptive Precision-EXpansion Kalman Filter), a track-following pipeline that makes mixed precision physics-aware. APEX-KF (i) assigns each track an initial FP16/FP32 (half/single precision) tier from a seed-momentum score before fitting and promotes mispredicted tracks at runtime (predict-then-guard); (ii) follows each track with one cooperating GPU warp whose 32 lanes evaluate candidate hits in parallel and select the minimum-χ² hit through a warp-shuffle reduction; and (iii) overlaps host-to-device transfers with computation across multiple CUDA streams while a roofline scheduler routes small events to the CPU. A deterministic FP16 emulator reproduces the GPU half-precision path bit-for-bit on any machine, making the precision study fully reproducible. On the public TrackML dataset (4,000 events, 1.05 × 10⁶ space points), APEX-KF keeps 60.8% of all track fits in FP16 while agreeing with the FP64 reference to 3.5 × 10⁻² GeV in pT—roughly 5 × 10² times closer than uniform FP16. The GPU back-end fits 8.8 × 10⁶ seeds on a laptop-class NVIDIA RTX 3050 in under one second, and the heterogeneous scheduler reduces device kernel time by 33%. Serial, OpenMP, and POSIX-threads back-ends return bit-identical physics, confirming the correctness of the parallel implementation.