Development of an equation free surrogate model using deep learning algorithm for heat transfer simulation

Abstract The Partial differential equations are one of the main tools in modeling many phenomena in real life. Since the formation and solving of the governing equations requires high processing time and computational costs. This study seeks to provide a method based on deep learning algorithms that can solve the equations independently of direct and numerical solution methods only by applying the boundary conditions of the problem on the neural network. This work explores the application of this paradigm on two-dimensional steady-state heat transfer equation. Due to the challenges of preparation large data with large dimensions, a novel method has been proposed to reduce the necessity of gathering data in large dimensions and size. In this method, first the steady-state heat transfer pattern encrypted in a kernel using thermal data in small size and dimensions. It is then used to train the steady-state predictor network without observing any steady-state heat transfer data simply by imposing restrictions on its outputs. This model was compared with a supervised model that trained by the large size of labeled data in the original dimensions. The result signifies that the proposed model has more accuracy, learning capability, and higher speed during the training stage.