Smart shape-morphing structures undergo controlled deformations in response to external stimuli and require inverse design strategies to achieve prescribed target shapes. While recent advances in additive manufacturing have enabled the realization of such systems, their design is often affected by multiple sources of uncertainty, including material properties, model inadequacy, and observation errors. In this work, we present an uncertainty-aware inverse design framework for shape-morphing structures based on Machine Learning and Probabilistic framework. The proposed approach integrates Approximate Bayesian Computation (ABC) to explicitly account for the modelling and parameter uncertainties within the inverse design process. As a case study, we consider a heterogeneous elastic tube embedding a gel core, whose shape change is driven by swelling-induced forces. Given a target shape, the algorithm determines the spatial distribution of the elastic tube’s material properties required to achieve the desired morphing. The sensitivity of the system to uncertain parameters, model inadequacy, and measurement noise is quantitatively analysed through posterior distributions. The results demonstrate that incorporating uncertainty significantly improves the robustness and reliability of ML-based inverse design, providing valuable insights for the development of shape-morphing systems with enhanced predictability.