I will start by discussing an idea and proof-of-concept to replace the exact amplitudes in Monte Carlo event generators with very precise approximate ones. This can be naturally achieved with machine learning algorithms and I will briefly discuss some algorithms that are ideally suited for this task.
The focus of the talk, however, will be on the remarkable progress since the proof-of-concept towards implementing this idea into the Monte Carlo generation pipeline. In particular, for the $qq\to ZZ\to 4\ell$ process which is of phenomenological interest at the LHC. I will discuss the necessary technology and various tradeoffs encountered in achieving this goal. For example, this includes leveraging the symmetries of the helicity amplitudes in order to build an optimal set of functions to approximate. The final result is that the two-loop virtual amplitude can be evaluated with percent or sub-percent precision in milliseconds. This translates to more than a thousandfold speedup over the exact amplitudes. Furthermore, I will show that the distribution of the approximation errors has very nice and advantageous properties. Finally, I will discuss the extension of this work to the full di-boson set of processes and to gluon-initiated two-loop matrix elements as well as some more ambitious goals of this program.