# Application of Soft Computing Techniques for Predicting Thermal Conductivity of Rocks
A methodology combining physical modeling and ML was proposed by [PERSON] et al. [42] to estimate the apparent ground thermal diffusivity at the national scale. In this methodology, a model is built with random forests (RF) using the output values from previous diffusivity estimations, as well as geological, elevation, and temperature features. The model, which exhibited an acceptable test error of 16.5%, is then used to estimate the apparent diffusivity across Switzerland. [PERSON], [PERSON], and [PERSON] [3] applied two ML techniques, including artificial neural networks (ANNs) and adaptive neuro-fuzzy inference (ANFIS), to predict TC by some series of datasets on rock properties (P-wave velocity, UCS, density, and porosity). The proposed models had a strong correlation coefficient between the measured and the predicted TC. [PERSON] et al. [43] used a multilayer perceptron (MLP) model to study concrete's thermal conductivity. A high degree of prediction accuracy was achieved by MLP. In this regard, [PERSON] [24] conducted an analysis using a feed-forward backpropagation neural network and found that the ANNs presented more accurate results than other techniques did. To predict the TC of Jalore granite, [PERSON] et al. [44] used artificial neural networks (ANNs), linear regression, support vector regressors (SVRs), and decision tree regressors (DTRs). According to their analysis, TC was strongly correlated with density, S-wave velocity, and P-wave velocity. Moreover, it was validated by different AI tools that thermal conductivity is highly sensitive to rock's physical properties [44]. In the study done by [PERSON] et al. [45], TC was analyzed using a convolutional neural network (CNN) and datasets of temperature fields from lattice Boltzmann method (LBM) simulations based on three-dimensional sphere-packed porous media. CNN and LBM acquired relative errors for the effective thermal conductivity of sphere-packed porous media (0.7-22.8%) and irregular porous media (3.1-16.0%). According to them, CNN is promising for the prediction of the heat transport properties of porous media with variable boundary conditions and different morphologies. For predicting geothermal gradient, thermal conductivity, the heat productivity of rocks, and the crustal/mantle heat flow, [PERSON] et al. [46] used generalized linear models(GLM), deep neural networks (DNN), and gradient-boosted regression trees (GBRT). Their results showed that the DNN model, with a number of neurons multiplied by the features, performed better than the other models. The average relative prediction errors for SVM and DNN were 13.3 and 12.7%, respectively. In a hybrid SVM-DNN approach, the average relative prediction error decreased to 12.2%. [PERSON] et al. [47] developed an ANFIS and a linear multivariable regression (LMR) model using 44 datasets that were collected from the literature. [PERSON] et al. [48] measured the thermal conductivity of various rocks in the Songliao Basin (China). The correlation between porosity, moisture content, density, P-wave velocity, and thermal conductivity were investigated. Seven prediction models were developed using extreme learning machine (ELM), support vector regression (SVR), and backpropagation neural network (BPNN) algorithms. The results demonstrated that the ELM-based model had better performance, speed, and accuracy for predicting rock thermal conductivity. The above-developed computer-aided models (ANNs and ANFIS) are black-box methods. Some pitfalls remained in these studies [49; 50]:  
* The relationship among the parameters was not determined, and the most critical parameters could not be identified [51]. * These models are not usable for field uses or future studies [51]. * The possibility of over-training or over-fitting in the training stages of ANNs and ANFIS is higher than it is when using white-box methods [51; 52].