Enhancing hydrogel predictive modeling: an augmented neural network approach for swelling dynamics in pH-responsive hydrogels

Abstract The pH-sensitive hydrogels play a crucial role in applications such as soft robotics, drug delivery, and biomedical sensors, as they require precise control of swelling behaviors and stress distributions. Traditional experimental methods struggle to capture stress distributions due to technical limitations, while numerical approaches are often computationally intensive. This study presents a hybrid framework combining analytical modeling and machine learning (ML) to overcome these challenges. An analytical model is used to simulate transient swelling behaviors and stress distributions, and is confirmed to be viable through the comparison of the obtained simulation results with the existing experimental swelling data. The predictions from this model are used to train neural networks, including a two-step augmented architecture. The initial neural network predicts hydration values, which are then fed into a second network to predict stress distributions, effectively capturing nonlinear interdependencies. This approach achieves mean absolute errors (MAEs) as low as 0.031, with average errors of 1.9% for the radial stress and 2.55% for the hoop stress. This framework significantly enhances the predictive accuracy and reduces the computational complexity, offering actionable insights for optimizing hydrogel-based systems.