Machine learning assisted inverse heat transfer problem to find heat flux in ablative materials

Thermal ablation of materials is a complex phenomenon that involves physical and chemical processes for the thermal protection of systems. However, due to the extreme thermal conditions and moving boundaries, predicting temperature and heat flux at the ablative material is quite challenging. A physics-informed neural network is a promising technique for many such inverse problems, including the prediction of unsteady heat flux. However, traditional physics-informed machine learning algorithms struggle with heat flux predictions in thermal ablation problems due to moving boundary conditions and lack of temperature data in the inaccessible domain. This study presents a hybrid approach, where an artificial neural network ( ANN ) is used for the accessible domain of the material and a physics-based numerical solution ( PNS ) technique is used in the inaccessible domain of the material, to find heat flux at the ablative surface. Temperature data at the accessible sensor points are used to train the ANN model. The heat flux at the ablative boundary was iteratively obtained from the numerical solution of the energy equation in the inaccessible domain by matching the ANN-predicted temperature at the last accessible sensor point. Our results indicate that this hybrid methodology significantly outperforms traditional physics-informed machine learning techniques, achieving excellent accuracy in predicting the temperature profiles and heat fluxes under complex conditions for both constant and variable heat flux and properties. By addressing the limitations of conventional physics-informed machine learning methods, our approach provides a robust and reliable solution for modeling the intricate dynamics of ablative processes. • A hybrid method is proposed combining artificial neural network and numerical model. • Only a few experimental data are needed to train the neural network in the hybrid model. • Unlike physics-informed neural networks, there is no convergence issue during training. • The boundary conditions at the inaccessible zone can be predicted with high accuracy. • The hybrid model can perform well even when noisy data are used in the training process.