Transport Equation based Physics Informed Neural Network to predict the Yield Strength of Architected Materials

Abstract: In this research, the application of the Physics-Informed Neural Network (PINN) model is explored to solve transport equation-based Partial Differential Equations (PDEs). The primary objective is to analyze the impact of different activation functions incorporated within the PINN model on its predictive performance, specifically assessing the Mean Squared Error (MSE) and Mean Absolute Error (MAE). The dataset used in the study consists of a varied set of input parameters related to strut diameter, unit cell size, and the corresponding yield stress values. Through this investigation the aim is to understand the effectiveness of the PINN model and the significance of choosing appropriate activation functions for solving complex PDEs in real-world applications. The outcomes suggest that the choice of activation function may have minimal influence on the model's predictive accuracy for this particular problem. The PINN model showcases exceptional generalization capabilities, indicating its capacity to avoid overfitting with the provided dataset. The research underscores the importance of striking a balance between performance and computational efficiency while selecting an activation function for specific real-world applications. These valuable findings contribute to advancing the understanding and potential adoption of PINN as an effective tool for solving challenging PDEs in diverse scientific and engineering domains.