Deep Learning-Aided Load and Response Prediction from Target Deformation of Soft Shell via Multitask U-Net

Inverse prediction from deformation to load and stress response is fundamental for real-time deformation control and structure health monitoring of soft devices, which, however, is critically challenging in the mechanics field due to the nonlinear mechanical behaviors. In this paper, we propose a multitask deep learning framework, i.e., a multitask U-Net (M-UNet) model, to inversely predict the distributions of both external force and internal stress components in a soft shell structure from the desired deformation patterns. The proposed M-UNet framework shows superior performance as the reconstructed deformations from predicted loads match target shapes with 0.39% relative error. Robustness and generalization of M-UNet are validated through additional finite element simulations by varying noise levels, load magnitudes and deformation smoothness in testing samples. Further demonstrations prove the low cost and highly efficient inverse design of external load distributions from a flat soft shell to arbitrary 3D shapes. M-UNet establishes a practical pipeline for inverse modeling using a multitask deep learning method, showing the great potential for structural optimization, real-time structural health monitoring and adaptive control systems of the next-generation soft devices. We hope this work provides insights into inverse problem studies in the mechanics of soft materials.