An inverse physics-informed neural network (I-PINN) framework for parameter estimation in mixed convection and melting effects

Abstract

An inverse physics-informed neural network (I-PINN) framework is developed for joint parameter estimation and field reconstruction in steady mixed convection with melting in a porous medium. Focusing on the laminar boundary layer of an Al2 O3 –Cu/water hybrid nanofluid over a vertical melting surface, the approach treats the mixed-convection parameter ? and the melting parameter M as trainable variables and fits sparse, noisy temperature measurements while satisfying the coupled similarity ODEs and boundary conditions. A robust training strategy combining data-guided curriculum learning, self-adaptive loss weighting, gradient clipping, and a hybrid Adam–L-BFGS optimization achieves accurate recovery and robust uncertainty quantification on synthetic benchmark data. The dominant parameter lambda is identified with below 0.5% relative error even with as few as eight sensors. The reconstructed temperature and velocity fields remain smooth and physically consistent across unmeasured regions. Notably, the method remains stable in the challenging opposing-flow regime near separation (lambda = -1.354, M = -0.4), demonstrating the promise of I-PINNs for parameter discovery, model calibration, and digital-twin development under limited data.