Two-stage physics-informed deep neural networks framework for form-finding of tensegrity structures

Abstract

This paper proposes a two-stage optimization deep neural network method for form-finding of tensegrity structures, based on physical information. The total loss function of the neural network is constructed by comprehensively considering the physical information, including nodal residual forces, element length constraints, and minimum node distance. To enhance the learning ability of the neural network, a two-stage optimization model is adopted. In the first stage, the AdamW optimizer is employed for preliminary training of the network's hyperparameters, quickly reducing the loss values. Following the preliminary training, the l-BFGS optimizer is utilized in the second stage to refine the optimization and converge toward the optimal solution, resulting in the nodal coordinates that satisfy the structural equilibrium. The paper includes case studies on five different tensegrity models. The results show that the proposed two-stage physics-informed deep neural network (PIDNN) approach, utilizing dual optimizers, can efficiently and accurately perform form-finding for various tensegrity structures, including both single- and multi-stable models. The method provides reliable results, avoids complex finite element computations, and offers high computational efficiency.