Physics-informed neural networks for inhomogeneous swelling analysis of dual-layer gels with chain entanglement effects

A field theory incorporating Edwards–Vilgis slip-link elasticity with Flory–Huggins mixing is developed for dual-layer gels containing rigid cores, capturing chain entanglement effects neglected by Neo–Hookean models. Physics-informed neural networks (PINNs) transform complexities of handling interfacial constraints into a neural network optimization problem, thereby reducing both algorithmic complexity and implementation requirements. Systematic parametric studies demonstrate that micromaterial parameters critically govern stress distributions, solvent concentration profiles, and swelling behavior. The framework enables precise control of target solvent concentrations and equilibrium configurations through optimal micromaterial parameter selection and thickness ratio design in dual-layer spherical gel systems.