Amplitude Surrogates for Multi-Jet Processes

TL;DR

This work develops a physics-informed neural surrogate for multi-jet amplitudes at LO by embedding Catani–Seymour dipole factorization into the surrogate design. The full amplitude A_n is factorized as A_n ≈ A_{n−1} · F_{ij,k}^r (and in a double-factorization variant as A_n ≈ A_{n−2} · F^{r} · F^{r′}), with a neural network learning a smooth correction factor c_{ heta} to recover the exact result, while operating in a standardized log-amplitude space using a heteroscedastic loss to quantify per-event reliability. The model supports multiple radiations, ranks them by singularity, and can ensemble multiple factorization variants to improve accuracy; a mixed strategy using surrogates only where uncertainty is acceptably small yields substantial speed-ups in LO event generation (up to around 20× in some cases) with controlled error budgets. This approach complements GPU acceleration and phase-space sampling, enabling scalable LO simulations for high-multiplicity final states and informing future extensions toward broader collider phenomenology and HL-LHC workloads.

Abstract

Accurate and efficient amplitude predictions are essential for precision studies of multi-jet processes at the LHC. We introduce a novel neural network architecture that predicts multi-jet amplitudes by leveraging the Catani-Seymour factorization scheme and related lower-jet amplitudes, requiring the network to learn only a correction factor. This hybrid approach combines theoretical factorization with a data-driven ansatz, enabling fast and scalable amplitude predictions. Our networks also estimate the accuracy of each prediction, allowing us to selectively use results that meet a predefined accuracy threshold. In the context of leading-order event generation, this approach achieves speed-up factors of up to 20 while maintaining all observables at the percent-level accuracy.

Figures (15)

• Figure 1: Approximation quality comparison between FG1, FG2, and FG3 radiations for $\mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \to \mathrm{Z}$Z$\xspace \mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace$ (left) and for $\mathrm{d}$d$\xspace \mathrm{\bar{d}}$d̅$\xspace \to \mathrm{Z}$Z$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace$ (right), obtained from unweighted samples.
• Figure 2: Approximation quality comparison between different radiation types: FG1, FQ1, IG1 and IQ1 radiations for $\mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \to \mathrm{Z}$Z$\xspace \mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace$ (left), and FG1, and IQ1 radiations for $\mathrm{d}$d$\xspace \mathrm{\bar{d}}$d̅$\xspace \to \mathrm{Z}$Z$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace$ (right), obtained from unweighted samples.
• Figure 3: Approximation quality comparison between single and double factorizations for $\mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \to \mathrm{Z}$Z$\xspace \mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace$ (left) and for $\mathrm{d}$d$\xspace \mathrm{\bar{d}}$d̅$\xspace \to \mathrm{Z}$Z$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace$ (right).
• Figure 4: Representation of the single factorization neural network.
• Figure 5: Single factorization model accuracy comparison between different radiation types (left), and different radiation ranks (right) for the process $\mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \to \mathrm{Z}$Z$\xspace \mathrm{d}$d$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace \mathrm{g}$g$\xspace$. The values in parentheses are the mean accuracies over the whole test dataset.