A combination of projection studies of non-resonant Higgs boson pair production is performed in the $b\bar{b}\gamma\gamma$ and $b\bar{b}\tau^+\tau^-$ decay channels with the ATLAS detector, assuming 3000 fb$^{-1}$ of proton-proton collision data at a center-of-mass energy of $\sqrt{s}$ = 14 TeV at the HL-LHC. The projected results are based on extrapolations of the Run 2 analyses conducted with 139$^{-1}$ data at $\sqrt{s}$ = 13 TeV. In addition to the increased luminosity and center-of-mass energy at the HL-LHC, both experimental and theoretical systematic uncertainties are expected to be reduced relative to their Run 2 values. The projected results are expressed in terms of the significance for the observation of the Standard Model Higgs boson pair production, and the constraint on Higgs boson trilinear self-coupling modifier $\kappa_\lambda$.