A centerline-based energy model for elastic ribbons based on neural networks

We report a simulation framework for elastic ribbons using a neural network-based one-dimensional energy model. The discrete elastic rods (DER) algorithm, originally developed to simulate 1-D rods, was repurposed to simulate elastic ribbons. The vanilla DER could not accurately capture the coupling between the bending and the twisting energies. The discrete elastic plates (DEP) framework, on the other hand, can accurately capture the mechanical behavior of ribbons. However, a plate-based simulation is computationally much more expensive than a rod-based method. For a physically accurate simulation in a computationally efficient manner, we use a neural network as the energy model for the centerline of a ribbon in a rod-like framework. DEP simulations are used to acquire ground truth time-series data of curvatures, twists, and stretch of the centerline of the ribbon under configurations involving bending and twisting. The neural network-based energy model is trained on these data using a neural ordinary differential equation (NODE) framework. Essentially, neural networks are reducing the energy model from 2-D in DEP to 1-D in DER, which leads to a reduced number of degrees of freedom and orders of magnitude computational speed up. Our approach can be taken as an inspiration to formulate non-linear dynamics of a system using neural networks, where it is difficult to capture non-linearity using analytical expressions. Our energy model can serve as a benchmark for future analytical energy models for ribbon.