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We investigate the Yukawa coupling unification for the third generation in aclass 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 theFermilab experiment E989. A recent analysis in supergravity grand unifiedmodels shows that such an effect can arise from supersymmetric loopscorrection. Using a neural network, we further analyze regions of the parameterspace where Yukawa coupling unification consistent with the Fermilab result canappear. In the analysis we take into account the contributions to Yukawas fromthe cubic and the quartic interactions. We test the model at the highluminosity and high energy LHC and estimate the integrated luminosities neededto discover sparticles predicted by the model.

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