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Constructing dynamical models for interacting pair of galaxies as constrainedby their observed structure and kinematics crucially depends on the correctchoice of the values of the relative inclination ($i$) between their galacticplanes as well as the viewing angle ($\theta$), the angle between the line ofsight and the normal to the plane of their orbital motion. We construct DeepConvolutional Neural Network (DCNN) models to determine the relativeinclination ($i$) and the viewing angle ($\theta$) of interacting galaxy pairs,using N-body $+$ Smoothed Particle Hydrodynamics (SPH) simulation data from theGALMER database for training the same. In order to classify galaxy pairs basedon 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 realdata 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 todetermine additional parameters needed to model dynamics of interacting galaxypairs, which is currently accomplished by trial and error method.

Determination of the relative inclination and the viewing angle of an interacting pair of galaxies using convolutional neural networks