Suburban trains ply between Chennai BEACH station and Velacheri. The journey takes 30 minutes from Central to Indira Nagar Station. The INDIRANAGAR station (the one before Tiruvanmiyur) is a few minutes' walk from IMSc. (However please do use the overbridge to cross unless youi have a death-wish!). If one is planning to catch the train for example from PARKTOWN station (the second station from Beach, which is a few minutes away from Chennai Central), one should take into account that the journey to Indiranagar will take 21 minutes.
Note that the above links to Southern Railway are not always very accurate.