Accounting for uncertainties in ML-based design of shape-morphing elements

Shape-morphing structures deform from one configuration to another in response to an external stimulus. In order to achieve a target shape, inverse design algorithms that enable one to compute the initial state of the system are required. Thanks to advances in 3D printing technologies, the realization of shape-morphing structures was demonstrated in a variety of recently published works. Commonly there are several sources of uncertainties that can influence the design. Examples include code inputs and outputs, model inadequacy, and the mechanical properties of 3D-printed materials. In this paper, we present an effective design of shape-morphing structures that accounts for these errors. We integrate a probabilistic approach to characterize model-form uncertainties in the inverse design of shape-morphing elements based on Machine Learning (ML) approach. The proposed approach relies on an Approximate Bayesian Computation (ABC) model where the parameter space is extended through the definition of the uncertainties involved in the process. To demonstrate the merit of this approach, we consider a system of a heterogeneous elastic tube embedding a gel core. The gel swells, and the swelling-induced forces lead to the deformation of the elastic tube, resulting in dilation and a change in the shape of the system. The proposed algorithm receives a target shape as input and determines the required spatial distribution of material properties in the heterogeneous ring. It is quantitatively shown how the system is sensitive to various sources of uncertainty: parameter uncertainty, model inadequacy, and observation errors. In particular, the effect of the parameter uncertainties has been investigated in terms of posterior distributions. In general, this work provides insight into the role of uncertainties in shape-controlled problems, and specifically, it allows for improving the reliability of the target shape inverse design in shape morphing elements.