Inferring identified hadron production in $pp$ collisions with physics-informed machine learning at the LHC

Machine learning has become a powerful tool in high-energy collider experiments, which enables the studies based on data-driven approaches to complex reconstruction and regression tasks. The study of identified hadron spectra in pseudorapidity regions beyond detector acceptance, which is limited to mid-rapidity regions, carries important information about particle production, yet remains unmeasured. In this work, we develop a physics-informed neural network, trained on PYTHIA8 $pp$ collisions at $\sqrt{s}=13.6$ TeV, to infer $p_{\rm T}$ spectra of $\pi^{\pm}$, $K^{\pm}$, $p/\bar{p}$, $\Lambda/\bar{\Lambda}$, and $K^{0}_{\mathrm{s}}$ in different rapidity regions. Physics-motivated constraints, including particle yield ratios, spectral shape, and smoothness, are incorporated into the loss function. A staged hyperparameter optimization strategy is used to ensure stability. The model achieves yield uncertainties of ${\sim}1.5\%$, $1.8\%$, and $5.83\%$ in the training, interpolation, and extrapolation regimes, respectively, outperforming XGBoost and LightGBM. It further reproduces key observables such as particle yield ratios, the multiplicity dependence of $\langle p_{\rm T} \rangle$, and kinetic freeze-out parameters, indicating that the model captures the underlying physics and provides reliable predictions beyond the measured phase space.