Comparative assessment of physics-informed recurrent networks for modeling rate- and density-dependent compression in expanded polystyrene foams

This study systematically compares Recurrent Neural Network architectures—namely simple Recurrent Neural Network, Long Short-Term Memory, and Gated Recurrent Units—for modeling the cyclic compressive mechanical response of Expanded Polystyrene foam across varying densities and loading rates. Purely data-driven (direct) methodologies and Physics-Informed Neural Network formulations, the latter with explicit physics enforcement, were investigated using experimental data from uniaxial cyclic compression tests. The objective was to predict the first Piola-Kirchhoff stress as a function of time, compressive stretch, initial density of the materials, and loading rate. Results demonstrated that direct Gated Recurrent Units and Long Short-Term Memory models consistently achieved the highest predictive accuracy, evidenced by low Mean Absolute Error and high coefficient of determination values, and exhibited superior generalization capabilities on unseen test conditions. While Physics-Informed Neural Network models, particularly those incorporating boundary conditions and energy restrictions, offered enhanced physical consistency—such as enforcing zero strain energy density at a unitary stretch and enforcing positive strain energy—they incurred greater computational expense and, in certain configurations, showed reduced predictive accuracy or stability, especially during generalization. The findings conclude that direct Gated Recurrent Units and Long Short-Term Memory architectures provide an effective and efficient approach for accurately capturing the complex, history-dependent behaviour of Expanded Polystyrene foam under cyclic loading.