  Determining the form of the Higgs potential is one of the most exciting
challenges of modern particle physics. Higgs pair production directly probes
the Higgs self-coupling and should be observed in the near future at the
High-Luminosity LHC. We explore how to improve the sensitivity to physics
beyond the Standard Model through per-event kinematics for di-Higgs events. In
particular, we employ machine learning through simulation-based inference to
estimate per-event likelihood ratios and gauge potential sensitivity gains from
including this kinematic information. In terms of the Standard Model Effective
Field Theory, we find that adding a limited number of observables can help to
remove degeneracies in Wilson coefficient likelihoods and significantly improve
the experimental sensitivity.
