Data-driven discovery of governing equations for transient heat transfer analysis

With the development of automatic measurement and data storage, vast quantities of data can be recorded and analyzed for heat transfer processes, which provides an opportunity to discover the transient heat transfer governing laws from the data. In this study, a machine learning-based sequential threshold ridge regression (STRidge) approach is applied to extract partial differential equations (PDEs) and tested on the heat conduction equation and conductive–convective heat transfer equation subjected to different boundary conditions, data volumes, and noise levels. Moreover, we studied the learning of governing equation of nonlinear transient heat transfer and used the improved STRidge with genetic algorithm to learn PDE with incomplete candidate library. The results showcase highly accurate identification of governing equations for heat transfer. And our results reveal the vast potential of the data-driven method in complex geothermal problems.