Index-Based Neural Network Framework for Truss Structural Analysis via a Mechanics-Informed Augmented Lagrangian Approach - Hyeonju Ha; Sudeok Shon; Seungjae Lee (Buildings)
This study proposes an Index-Based Neural Network (IBNN) framework for the static analysis of truss structures, employing a Lagrangian dual optimization technique grounded in the force method. A truss is a discrete structural system composed of linear members connected to nodes. Despite their geometric simplicity, analysis of large-scale truss systems requires significant computational resources. The proposed model simplifies the input structure and enhances the scalability of the model using member and node indices as inputs instead of spatial coordinates. The IBNN framework approximates member forces and nodal displacements using separate neural networks and incorporates structural equations derived from the force method as mechanics-informed constraints within the loss function. Training was conducted using the Augmented Lagrangian Method (ALM), which improves the convergence stability and learning efficiency through a combination of penalty terms and Lagrange multipliers. The efficiency and accuracy of the framework were numerically validated using various examples, including spatial trusses, square grid-type space frames, lattice domes, and domes exhibiting radial flow characteristics. Multi-index mapping and domain decomposition techniques contribute to enhanced analysis performance, yielding superior prediction accuracy and numerical stability compared to conventional methods. Furthermore, by reflecting the structured and discrete nature of structural problems, the proposed framework demonstrates high potential for integration with next-generation neural network models such as Quantum Neural Networks (QNNs).