Abstract: An analysis of geometric defects in plate assembly under linear-elastic conditions is investigated. A hybrid FEM–PINN (MDR) model is proposed, combining the finite element method, the analytical dimensionality reduction method, and physics-informed neural networks. This approach enables the coupling of physics-based modeling with data-driven learning. PINNs explicitly incorporate governing physical laws, including constitutive relations and contact conditions, into the training process using the dimensionality reduction method solutions, thereby ensuring the physical consistency of the predicted responses. This integration provides a trade-off between high-fidelity numerical modeling and reduced computational complexity. Additionally, the use of machine learning enhances computational efficiency while maintaining robustness, accuracy, and reliability in analyzing mechanical assemblies. The methodology is validated through a case study of a simple linear-elastic component assembly, and the results are given and discussed to demonstrate its effectiveness.

Key words: Flexible assembly, Fem, Physics neural networks, Dimensionality reduction.