Isolate mesh-extent and particle-count contributions to gradient-matching bias

Isolate the separate contributions of PIC node count, macroparticle count, and grid extent to the coarse-model bias in HELIX differentiable gradient matching, and re-cost matched solutions using a wider grid extent.

Background

The differentiable matching path uses a coarse default PIC configuration of a $32^3$ grid, an adaptive $\pm4\sigma$ extent, and 1500 macroparticles, while higher-fidelity revalidation uses a $64^3$ grid and 5000 particles. The revalidation shows that the remaining mismatch is dominated by bias in the coarse optimization model rather than by optimizer error.

The paper reports that the node-count and particle-count changes were varied together, while the grid extent was not varied in the revalidation. Although a separate stress test indicates that grid extent can strongly affect rms sizes, the individual contributions of these numerical choices to the matching bias remain unresolved. The authors therefore identify their isolation and the cost of wider-extent revalidation as an open item.