We investigate error growth from small-amplitude initial condition perturbations, simulated with a recent artificial intelligence-based weather prediction model. From past simulations with standard physically-based numerical models as well as from theoretical considerations it is expected that such small-amplitude initial condition perturbations would grow very fast initially. This fast growth then sets a fixed and fundamental limit to the predictability of weather, a phenomenon known as the butterfly effect. We find however, that the AI-based model completely fails to reproduce the rapid initial growth and hence would suggest an infinite predictability of the atmosphere. In contrast, if the initial perturbations are large and comparable to current uncertainties in the estimation of the initial state, the AI-based model basically agrees with physically-based simulations, although some deficits are still present.