Physics-informed neural networks for studying heat transfer in porous media

Numerous efforts have been devoted to studying heat transfer problems in porous media. Physics-based models, numerical methods and experiments are commonly adopted to obtain the temperature and heat flux fields, along with effective thermophysical properties like effective thermal conductivity for heat conduction, which exert significant impact on analyzing the heat transfer efficiency in porous systems. Recently, using data-driven machine learning methods to predict temperature/heat flux fields and effective thermal conductivity of porous media has gained attention, demonstrating the potential to achieve higher accuracy than physics-based models while requiring less computational time than numerical methods. However, machine learning approaches are commonly restricted by the requirement for sufficient labeled training data, which can be difficult and time-consuming to acquire. In this work, we apply physics-informed neural networks to investigate heat conduction in porous media. We show that, without any labeled training data, accurate predictions for temperature/heat flux fields in porous media can be achieved. The obtained effective thermal conductivity values for an ensemble of porous media samples have an average relative error of only 2.49%. Compared with numerical calculations, a computation acceleration of 5 orders of magnitude has been achieved. Compared with data-driven machine learning methods, this method offers enhanced flexibility since no labeled data is required. Furthermore, we also illustrate that physics-informed neural networks can be easily extended to predict nonlinear heat conduction in porous media. Our work demonstrates that physics-informed neural networks are promising tools for studying heat conduction problems and can also be possibly extended to study other complex heat transfer problems in porous media.