Development of an Equation Free Reduced Order Model Based on Different Approaches of Feature Extraction for Two-dimensional Steady State Heat Transfer Data Set

Since the formation and Direct solving the governing equations requires high time and computational cost, this study seeks to provide an equation free model based on deep learning algorithm that simulates steady state heat transfer in two-dimensional space and a relatively large size using order reduction method. Principal component analysis is a linear method and autoencoder is a nonlinear methods. The results of comparing their performance on different data sets showed that in reducion of order to very low dimensions, autoencoder and in reducion of order to very high dimensions, principal component analysis has a higher accuracy. Of course, the number of dimensions to order reduction and the characteristics of the data set such as size and number of dimensions of the data will affect the accuracy of the dimensional reduction. These two methods were used to order reduction of thermal data in order to faster simulate the phenomenon of Steady State Heat Transfer and were compared with a model based on convolutional neural network with a number of layers and multiple filters. The results showed that the models based on order reduction methods have much less computational volume and simulation time, and the outputs obtained from them, especially the model based on the autoencoder method, have a much higher accuracy.