Physics-guided artificial intelligence for latent heat transfer in phase-change material walls: comparison between universal differential equations and the Fourier neural operator

This study investigates the prediction of thermal behavior in cement mortar walls incorporating bio-based phase change materials (PCM), using two advanced deep learning frameworks: Universal Differential Equations (UDE) and Fourier Neural Operators (FNO). A physical experiment was conducted on a cement mortar wall containing 11 wt% of microencapsulated PCM. This wall was instrumented with thermal sensors at three different depths and subjected to controlled boundary conditions. The UDE approach integrates an enthalpy-based physical model with a neural correction term to capture latent heat dynamics, while also utilizing learnable thermophysical parameters and an adaptive multiple shooting strategy to prevent numerical drift. Conversely, FNO learns to predict entire temperature fields directly from experimental data by operating in the Fourier domain. Results show that both models achieve high predictive accuracy. The optimized UDE model demonstrates superior performance at the sensor locations with a global RMSE of 0.0399 °C and an R 2 of 0.9999, compared to an RMSE of 0.1680 °C and an R 2 of 0.998 for the FNO. These findings highlight the comparable accuracy of both frameworks, while the UDE offers the added benefit of a physically interpretable model with embedded and calibrated thermophysical parameters.