Physics-Informed Graph Neural Networks for Transverse Momentum Estimation in CMS Trigger Systems

Real-time particle transverse momentum ($p_T$) estimation in high-energy physics demands algorithms that are both efficient and accurate under strict hardware constraints. Static machine learning models degrade under high pileup and lack physics-aware optimization, while generic graph neural networks (GNNs) often neglect domain structure critical for robust $p_T$ regression. We propose a physics-informed GNN framework that systematically encodes detector geometry and physical observables through four distinct graph construction strategies that systematically encode detector geometry and physical observables: station-as-node, feature-as-node, bending angle-centric, and pseudorapidity ($η$)-centric representations. This framework integrates these tailored graph structures with a novel Message Passing Layer (MPL), featuring intra-message attention and gated updates, and domain-specific loss functions incorporating $p_{T}$-distribution priors. Our co-design methodology yields superior accuracy-efficiency trade-offs compared to existing baselines. Extensive experiments on the CMS Trigger Dataset validate the approach: a station-informed EdgeConv model achieves a state-of-the-art MAE of 0.8525 with $\ge55\%$ fewer parameters than deep learning baselines, especially TabNet, while an $η$-centric MPL configuration also demonstrates improved accuracy with comparable efficiency. These results establish the promise of physics-guided GNNs for deployment in resource-constrained trigger systems.