  We use theory and first-principles calculations to investigate how structural
changes induced by ultrafast optical excitation of infrared-active phonons
change with hydrostatic pressure in LaAlO$_3$. Our calculations show that the
observed structural changes are sensitive to pressure, with the largest changes
occurring at pressures near the boundary between the cubic perovskite and
rhombohedral phases. We rationalize our findings by defining a figure of merit
that depends only on intrinsic materials quantities, and show that the peak
response near the phase boundary is dictated by different microscopic materials
properties depending on the particular phonon mode being excited. Our work
demonstrates how it is possible to systematically identify materials that may
exhibit particularly large changes in structure and properties due to optical
excitation of infrared-active phonons.
