Deep Spring: Inverse Design of Suspended Elastic Rods using Physics-Informed Neural Networks

Accurately predicting the geometrically nonlinear deformation of slender structures has been extensively studied across different scientific disciplines, such as mechanics and computer graphics. Our structure of interest is rods, which are unique structures that are prone to large deformation even under small loading, e.g., its own weight. The forward problem of predicting the deformation of rods can be readily addressed with efficient frameworks such as Discrete Elastic Rods (DER). However, the inverse problem of finding the initial geometry that deforms into the target shape is a highly nonlinear optimization problem. Previously, by capitalizing on the availability of inexpensive data generated through DER, we have introduced the concept of Deep Spring methodology to tackle the inverse problem for beams. Here, we extend our methodology to three-dimensional rods, which contain a higher level of complexity in their geometry due to the concept of twisting. Moreover, we implement a physics-informed structure to our neural network, which imposes satisfaction of the work-energy theorem to the predicted geometry.