  In material modeling, the calculation speed using the empirical potentials is
fast compared to the first principle calculations, but the results are not as
accurate as of the first principle calculations. First principle calculations
are accurate but slow and very expensive to calculate. In this work, first, the
H-H binding energy and H$_2$-H$_2$ interaction energy are calculated using the
first principle calculations which can be applied to the Tersoff empirical
potential. Second, the H-H parameters are estimated. After fitting H-H
parameters, the mechanical properties are obtained. Finally, to integrate both
the low-fidelity empirical potential data and the data from the high-fidelity
first-principle calculations, the multi-fidelity Gaussian process regression is
employed to predict the H-H binding energy and the H$_2$-H$_2$ interaction
energy. Numerical results demonstrate the accuracy of the developed empirical
potentials.
