Particle collisions at the LHC produce events across an enormous range of energies, and no single Monte Carlo simulation covers the whole span. The work here trains one transformer-based generative model spanning five decades of invariant mass, from below a GeV to the TeV continuum.

The physics is built into the model's geometry rather than hoped for in its outputs. ShellFlow uses Riemannian conditional flow matching and generates each particle on its on-shell manifold, meaning the mass-energy relation a real particle must satisfy holds by construction. A model free to produce anything would have to learn that constraint approximately from data and would still violate it occasionally.

That is a recurring theme in scientific machine learning: where a hard constraint is known, encoding it in the space the model works over is usually better than penalising violations after the fact.