How to bond polymer to polymer (TPU on PMMA)
Sorry to say but you question is a bit vague because without knowing the project, it's pretty hard to help. Anyway, here is some general information.
Some of the sophisticated methods of joining these together include solvent bonding, vibration welding, friction welding and induction welding or pressure sensitive adhesives [ (Meth)acrylic copolymers are one of the most widely used polymer classes for the production of pressure-sensitive adhesives]. Acrylic requires an acrylic solvent adhesive. Cyanoacrylate (super glue) may work, depending on the project. UHU glue is very useful with all kinds of plastics, so you might wanna try that.  I myself have tried superglue and it works with both materials. But I think for your project, non adhesive methods woll be an optimal choice.
All the best.