Actually, yes ! There is a marvelous paper of A. Pouly, O. Bournez et al. which described a connection between turing machine and ODE. And this connection preserve the notion of polynomiality by looking at the length of the function that solve the ODE. This means that the notion of polynomiality of a problem can be linked directly to properties of ODE independently of any machine or whatever. For one of their article see: https://dl.acm.org/doi/abs/10.1145/3127496

Yes, via Ordinary Differential Equations.

Bournez et al. described a connection between Turing Machines and Ordinary Differential Equations (ODE). Such connection preserves the notion of polynomiality by looking at the length of the function that solves the ODE. This means that the notion of polynomiality of a problem can be linked directly to properties of ODE independently of any machine or whatever.