Physics-constrained graph closures and working-point conditioning for a fast surrogate of linac beam dynamics

Abstract

When a graph neural network estimates a physical quantity, its frame, edge direction, aggregation and feature normalization decide which laws it can break. Wrong choices leave systematic errors the loss never registers. We build a linac beam-dynamics surrogate on this observation. Space charge, short-range wakefields and coherent synchrotron radiation enter as bounded closures on analytic kernels, on graphs whose frame and direction follow the interaction and whose symmetry makes the net space-charge self-force vanish for any weights. Verified without training, with randomized weights, the invariants break by five to eight orders of magnitude once the responsible feature is inverted. Per-working-point models constrained by the rms envelope equation are distilled into one model conditioned on 15 machine settings. On the 18.4~m L0+L1 section of the Shanghai soft x-ray free-electron laser linac, this model predicts the transverse beam envelope at 50 unseen settings to about $7\%$, with the centroid trajectory and emittance, in 0.38~s on a single Quadro RTX 6000 GPU. Training is instead dominated by a normalization choice, a data-derived output range for the beam size: at all 16 working points it lowers the starting error 2.2- to 8.5-fold and fixes the convergence speed. The remaining accuracy differences between hybrid and data-driven architectures vary with the working point and with the density of observation. The held-out error scales roughly as $N^{-0.6}$ with the corpus size $N$. Whether the physics pays off where collective effects are strong, as in a magnetic bunch compressor, is in the next phase of our study.