  To develop a quantitative reaction simulator, data assimilation was performed
using high-resolution time-of-flight mass spectrometry (TOF-MS) data applied to
GaN metalorganic vapor phase epitaxy system. Incorporating ab initio knowledge
into the optimization successfully reproduces not only the concentration of
CH$_4$ (an impurity precursor) as an objective variable but also known reaction
pathways. The simulation results show significant production of GaH$_3$, a
precursor of GaN, which has been difficult to detect in TOF-MS experiments. Our
proposed approach is expected to be applicable to other applied physics fields
that require quantitative prediction that goes beyond ab initio reaction rates.
