Buying a copy of a TV series doesn't give you any additional rights to use it for training a model. It just gives you a right to possess the copy, and to watch it. If you do train a model, and don't break any DRM / technological protection measures (in the US), and you don't distribute the model or anything generated by it, then it's ok. What you do with it at home is your business. If you do distribute it then...??? Nobody knows for sure about the legality, because it hasn't been tested thoroughly in the courts.

If your work is non-commercial, and has no potential impact on the sales of the TV series, or other economic damage to anyone, there is very little trouble you could get into. It may be seen as "fair use", though that's not a guarantee right now. The worst would be a "cease and desist" or DMCA takedown order, from the lawyers of the rights holders of the show. How likely that is to happen, or succeed if you challenged it in court, would depend on the details of your specific case.