Physics-Informed Neural Networks for Thermo-Responsive Hydrogel Swelling: Integrating Constitutive Models with Sparse Experimental Data

Poly(N-isopropylacrylamide) (PNIPAM) hydrogels are temperature-sensitive materials whose swelling is difficult to predict near the gel collapse temperature (GCT). A physics-informed neural network (PINN) was developed in which a stabilized free-energy model is embedded and sparse data for free and uniaxially constrained swelling are assimilated. Across datasets, the PINN reduces test RMSE by 44% at low crosslink density (Nν = 0.0035) and by 65% at higher density (Nν = 0.02), with coverage inside ±RMSE bands improving from 61.9% to 76.2% for free swelling at Nν = 0.0035. Under constraint, test relative error decreases from 19.95% to 11.86% (n = 1) and from 9.19% to 5.90% (n = 3), while preserving thermodynamic stability. The method sharpens the transition slope near the gel-collapse temperature and narrows prediction intervals without overfitting, capturing cold-regime plateaus and hot-side tails more faithfully. The framework integrates governing equations with data to deliver accurate swelling and stress predictions using only eight anchors and thirteen held-out points per case. These results position PINNs as a reliable surrogate for designing thermo-responsive hydrogels in soft actuators and biomedical systems.