Yukawa coupling unification in an $\mathsf{SO(10)}$ model consistent with Fermilab $(g-2)_{\mu}$ result

We investigate the Yukawa coupling unification for the third generation in a class of $\mathsf{SO(10)}$ unified models which are consistent with the 4.2 $\sigma$ deviation from the standard model of the muon $g-2$ seen by the Fermilab experiment E989. A recent analysis in supergravity grand unified models shows that such an effect can arise from supersymmetric loops correction. Using a neural network, we further analyze regions of the parameter space where Yukawa coupling unification consistent with the Fermilab result can appear. In the analysis we take into account the contributions to Yukawas from the cubic and the quartic interactions. We test the model at the high luminosity and high energy LHC and estimate the integrated luminosities needed to discover sparticles predicted by the model.