Physics-Informed Deep Learning for Modeling of Cylindrical Shells

Abstract

This study revisits the canonical problem of the structural response of a cylindrical shell under hydrostatic pressure using physics-informed neural networks. Particular attention is given to the strong formulation of the governing differential equation, which poses significant challenges due to the need for accurate evaluation of higher-order derivatives. To enforce boundary conditions, a modified loss function with embedded hard constraints is proposed. The model hyperparameters are identified through a series of numerical experiments. The results indicate that physics-informed neural networks may exhibit inherent limitations that hinder their ability to accurately capture all features of the exact solution. To address these limitations, a hybrid approach integrating physics-based modeling and statistical learning theory via ensemble techniques is proposed. The ensemble framework demonstrates improved generalization and reliability, suggesting its potential to enhance the performance of physics-informed neural networks in solving differential equations.