Optimization of Neural Network architecture and derivation of closed-form equation to predict ultimate load of functionally graded material plate

Functionally Graded Material (FGM) plate is a complicated structure with complex allocation of spatially changing proportions of ceramic and metal within the matter. Various analytical and numerical methods have been applied with a view to evaluating the critical load of FGM plate. However, these conventional methods struggle when the computational complexity is significant, which represents an obstacle to incorporation with other advanced techniques where computational power is required (e.g. optimization or random simulations). The Neural Network (NNet) model has been successfully applied to resolve this issue. However, the conventional NNet requires proper configuration to take advantage of the model, and thus, careful parameter tuning is required. Furthermore, the NNet is typically a black box, where the prediction mechanism is hidden. This paper establishes an optimized architecture for NNet, with parametric study of the model's hyperparameters. Variance propagation is also applied to observe the variation of the model's performance on random sub-databases splintered from the database. To this end, the explicit expression of the trained NNet model is provided after mathematically deploying the hidden algebra behind an NNet prediction. The developed model has very promising evaluation metrics: R-2, MAE, and RMSE on the test set are 0.999925, 0.067516, and 0.146438, respectively.

Automated summary

Functionally Graded Material (FGM) plates are complex structures with changing proportions of ceramic and metal. Conventional methods struggle with computational complexity, hindering incorporation with advanced techniques. The Neural Network (NNet) model is successfully applied, but requires proper configuration and parameter tuning. This paper establishes an optimized NNet architecture, studies hyperparameters, and provides an explicit expression for the trained model. The model shows promising evaluation metrics with high R-2, low MAE, and low RMSE values on the test set.