Physics-based Inverse Design of Elastic Rods with Deep Neural Network

Rod-like structures, such as DNA, climbing plants, and cables, pervade the nature and our daily life, which usually assume a deformed shape based on the competition between elastic (stretching, bending, twisting) and external (e.g. gravity) forces. We take a combination of physics-based and machine learning-driven approach to tackle the problem of obtaining the undeformed shape, given the deformed configuration under gravity. Conventional methods typically couple a numerical simulation of the elastic rods with optimization subroutines. We focus on rapidly solving the inverse problem in real-time using the Discrete Elastic Rods (DER) algorithm to simulate the forward problem and deep neural networks (DNNs) to store a large number of solutions. However, problems involving very long rods cannot be stored in DNNs due to the requirement of vast training dataset and insufficient precision in complex regression problems. We overcome this issue by decomposing a large rod into a series of smaller parts; the solution involving the smaller parts are stored in DNNs. Using the balance of forces and moments at the joints between two smaller parts, these smaller solutions are combined together to construct the larger solution.