On the use of mechanics-informed models to structural engineering systems: Application of graph neural networks for structural analysis

This paper investigates the application of mechanics-informed artificial intelligence to civil structural systems. Structural analysis is a traditional practice that involves engineers to solve different real-life problems. Several approaches can be used for this task, going from "by hand" computation to the recent advanced finite element method. However, when structures become complex, the success of the analysis can be complicated, often requiring high computational efforts and time. To tackle this challenge, traditional high-demanding methods can be supported by new technologies, such as machine-learning tools. This new paradigm aims to solve structural problems by defining the desired output after directly elaborating input data. One of the current limitations is that often the physics behind the problem is ignored. To solve this issue, resolution models can combine empirical data and available mechanics prior knowledge to improve the predictive performance involving physical mechanisms. In this paper, a method to develop a Mechanics-Informed Surrogate Model (MISM) on structural systems is proposed, for which input structured data are used to enrich the informative content of mechanics systems. Then, Graph Neural Networks (GNNs) are explored, as a method capable of properly rep-resenting and embedding knowledge about a structural system, such as truss structures. The main advantage of the proposed approach is to provide an alternative way to the usual black-box machine-learning-based models. In fact, in the proposed MISM, the mechanics of the structural system plays the key role in the surrogate model definition, in order to obtain physically based outputs for the investigated problem. For the case at hand, MISMs are developed and employed to learn the deformations map of the system, starting from the knowledge of the structural features. The proposed approach is applied to bi-dimensional and tri-dimensional truss structures and the results indicate that the proposed solution performs better than standard surrogate models.