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, and 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; the graphs carry a frame and a direction dictated by the interaction; and their 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%, together 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.
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BibTeX
@misc{zhang2026physicsconstrained,
title = {{Physics-constrained graph closures and working-point conditioning for a fast surrogate of linac beam dynamics}},
author = {Bowen Zhang and Dazhang Huang and Nengyuan Zhang and Duan Gu and Chao Feng and Bo Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28250},
eprint = {2610.28250},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28250},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Physics-constrained graph closures and working-point conditioning for a fast surrogate of linac beam dynamics
AU - Bowen Zhang
AU - Dazhang Huang
AU - Nengyuan Zhang
AU - Duan Gu
AU - Chao Feng
AU - Bo Liu
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.28250
UR - https://arxiv.org/abs/2610.28250
AB - When a graph neural network estimates a physical quantity, its frame, edge direction, aggregation and feature normalization decide which laws it can break, and 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; the graphs carry a frame and a direction dictated by the interaction; and their 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%, together 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.
ER -