Physics-Constrained Neural Network with Inverse Transform Sampling for Temperature-Humidity Coupling Effects on Cavitation in Thermo-Responsive Elastomeric Gels

This work presents a novel computational framework for analyzing cavitation phenomena triggered by environmental temperature and humidity in thermo-responsive elastomeric gels. We demonstrate that cavitation instabilities, originating from pre-existing defects, exhibit discontinuous cavity expansion under permeable boundary constraints in swollen gels. Through variational methods, constitutive equations are achieved based on equilibrium thermodynamics of elastomeric gels. Physics-constrained neural network with inverse transform sampling (ITS-PCNN) is developed to approximate the solution to the governing equation, which demonstrates superior stability and accuracy compared to conventional physics-informed neural networks (PINN), achieving consistently lower residual norms for both geometric and equilibrium equations. The ITS-PCNN framework enables comprehensive investigation of the coupling effects of temperature and humidity on cavitation behavior in thermo-responsive elastomeric gels. Our findings establish a robust computational platform for predicting cavitation responses under varying environmental conditions, advancing the design of responsive materials for biomedical and microfluidic applications.