Efficient Prediction of Equivalent Thermo-Mechanical Properties for Embedded Unit Cells in Reliability Simulations of Complex Circuit Wiring Structures Using a Transformer-CNN Model

In the field of reliability simulation and analysis of complex circuit wiring structures, the remarkable effectiveness of the Convolutional Neural Network (CNN) in wiring diagram recognition has shown great potential for predicting the equivalent performance of partitions of complex wiring structures. Considering the heavy computational burden of simulation and the fact that the planes of complex wiring structures have long-range disordered and short-range ordered structural features, it is necessary to consider the influence of the long-range surroundings on their short-range partitions, which can be achieved by using the Embedded Unit Cell (EUC) modelling approach. Simply applying a CNN model can capture the wiring features, but it cannot accurately learn the relationship between such central regions in complex wiring structures that are influenced by the surrounding regions. This paper introduces a Transformer-CNN hybrid deep learning model, which extracts local features from partitioned wiring diagrams using CNN and employs a Transformer to learn the relationships among them through a self-attention mechanism, and finally discusses the learning accuracy and efficiency. This method aims to create a more efficient process for predicting the equivalent thermo-mechanical properties of EUC partitions in reliability simulations of wiring structures. The results demonstrate that the model performs excellently in terms of prediction accuracy and efficiency. The model predicts that the coefficient of determination (R2) between the values of four types of anisotropic equivalent thermo-mechanical properties (Young's modulus, shear modulus, Poisson's ratio, and coefficient of thermal expansion) and the results of simulation are all higher than 0.99, a Mean Absolute Error (MAE) less than 0.000646, indicating the model's ability to accurately learn and map equivalent thermo-mechanical property values from the wiring diagrams. Handling over 260,000 datasets, the model required 29 hours for training and only 1 hour for prediction, less than one-tenth the time needed for simulations, enhancing the efficiency of the EUC modeling method for engineering reliability analysis of complex circuit wiring structures.