Multiphysics-informed deep learning for swelling of pH/temperature sensitive cationic hydrogels and its inverse problem

This paper proposes a field theory of constrained swelling of pH/temperature sensitive cationic hydrogels in equilibrium with their chemical and mechanical environment. A general formulation is obtained based on a variational approach, yielding a set of governing equations coupling mechanical and chemical equilibrium conditions, which is employed to investigate some benchmark problems involving homogeneous and inhomogeneous swelling of the pH/temperature sensitive cationic hydrogels. The simulation results are compared with experimental data available in the literature to verify the present model. By encoding the underlying physical and chemical laws into the deep learning neural networks as prior information, we introduce the multiphysics-informed deep learning (MIDL) to investigate the effects of temperature and pH on the distributions of concentration of solvent and stresses in the hydrogel shell. In addition, the MIDL is extended to solve inverse identification problem of inhomogeneous swelling of core-shell hydrogels, which yields a reasonable identification accuracy even if the observed data is corrupted due to uncorrelated noise.