  Constructing dynamical models for interacting pair of galaxies as constrained
by their observed structure and kinematics crucially depends on the correct
choice of the values of the relative inclination ($i$) between their galactic
planes as well as the viewing angle ($\theta$), the angle between the line of
sight and the normal to the plane of their orbital motion. We construct Deep
Convolutional Neural Network (DCNN) models to determine the relative
inclination ($i$) and the viewing angle ($\theta$) of interacting galaxy pairs,
using N-body $+$ Smoothed Particle Hydrodynamics (SPH) simulation data from the
GALMER database for training the same. In order to classify galaxy pairs based
on their $i$ values only, we first construct DCNN models for a (a) 2-class (
$i$ = 0 $^{\circ}$, 45$^{\circ}$ ) and (b) 3-class ($i = 0^{\circ}, 45^{\circ}
\text{ and } 90^{\circ}$) classification, obtaining $F_1$ scores of 99% and 98%
respectively. Further, for a classification based on both $i$ and $\theta$
values, we develop a DCNN model for a 9-class classification ($(i,\theta) \sim
(0^{\circ},15^{\circ}) ,(0^{\circ},45^{\circ}), (0^{\circ},90^{\circ}),
(45^{\circ},15^{\circ}), (45^{\circ}, 45^{\circ}), (45^{\circ}, 90^{\circ}),
(90^{\circ}, 15^{\circ}), (90^{\circ}, 45^{\circ}), (90^{\circ},90^{\circ})$),
and the $F_1$ score was 97$\%$. Finally, we tested our 2-class model on real
data of interacting galaxy pairs from the Sloan Digital Sky Survey (SDSS) DR15,
and achieve an $F_1$ score of 78%. Our DCNN models could be further extended to
determine additional parameters needed to model dynamics of interacting galaxy
pairs, which is currently accomplished by trial and error method.
