Physics-informed neural networks for planar interface evaporation: Forward, inverse, and parameterized modeling

In this work, we develop physics-informed neural networks (PINNs) to model two-phase evaporation of a planar liquid-vapor interface by solving the unsteady one-dimensional Stefan problem in forward, inverse, and parameterized settings. The governing physics formulation couples the vapor volume-of-fluid (VOF) transport equation with the mixture energy equation through heat and mass transfer source terms. To enable stable coupling with a diffuse-interface and an energy-jump-based phase change model, we introduce a modified energy-intensity transfer source term. For the forward problem, the deep neural networks are trained solely from the governing physics and the prescribed initial and boundary conditions, without requiring labeled solution data. The forward PINNs solver is systematically evaluated with respect to collocation-point resolution, the energy-intensity coefficient, and the critical vapor volume fraction threshold, and it demonstrates robust predictions with minimal sensitivity to these training and model parameters. In addition, the framework accurately captures sharp interface motion associated with strong interfacial temperature gradients. Forward predictions of interface evolution and temperature fields under varying boundary conditions and phase properties agree closely with analytical solutions across all cases. For the inverse problem, a data-driven term based on VOF profiles from theoretical solutions is incorporated into the total loss. The inverse PINNs framework is then used to infer unknown boundary conditions (wall superheat temperature) and thermophysical properties (vapor thermal conductivity and latent heat) during training. The inferred parameters are recovered with errors below 7%, even in the presence of measurement noise. Finally, we extend the approach to training across a multidimensional parametric space to produce full field temperature and phase VOF solutions, highlighting its potential over traditional two-phase modeling methods.