Intelligent evaluation and interpretable attribution analysis of geothermal potential of sandstone thermal storage driven by ViT-KAN model

Sandstone thermal storage geothermal resources are clean, stable and renewable, which is of great significance to the transformation of regional energy structure under the goal of "double carbon". However, the complex geological conditions, strong heterogeneity of thermal storage and exploration uncertainty still make the accurate assessment of regional geothermal potential face challenges. In this paper, Beiping, western Shandong Province was taken as the research area, and the geological structure conditions and thermal storage characteristics were comprehensively considered. Ten evaluation indexes, such as elevation, slope and water depth, were selected, and Pearson correlation coefficient and variance expansion factor were used to carry out feature screening. Combining KAN(Kolmogorov-Arnold Networks) and ViT(Vision Transformer), a ViT-KAN model for evaluating the potential of geothermal resources in sandstone thermal storage is constructed, and eight indicators, such as receiver operating characteristic curve area, accuracy and recall rate, are selected from two dimensions of classification discrimination ability and probability prediction accuracy to evaluate the performance of the model. Combining SHAP (Shapley Additional Explanations) and counterfactual analysis method, the key controlling factors of geothermal resources potential are revealed. The results show that there are multiple collinearities between the buried depth of floor and the thickness of thermal storage, which are eliminated after feature screening to reduce the redundancy of input features. By comparing the changing trends of Loss and AUC in the training process, the Loss of the test set of ViT-KAN decreased to 0.334, and the AUC reached 0.936, both of which were better than those of ViT's 0.365 and 0.914, and the convergence was more stable, indicating that the introduction of KAN can effectively optimize the training process and improve the prediction accuracy. Compared with ViT, ViT-KAN has higher AUC, ACC and Recall in training set and test set, lower MSE, RMSE and MAE, and the overall ROC curve is dominant (AUC in test set is 0.936, RMSE is 0.401), and its classification discrimination ability and prediction error control are better than Vit. The classification of geothermal potential based on natural discontinuity method shows that the overall spatial pattern predicted by the two models is consistent, and the high-potential areas are concentrated in Decheng District, Lingcheng District and Pingyuan County in the north, but ViT-KAN describes the high-potential areas more finely, with the extremely low and low potential areas accounting for 49.2% in total, while ViT has raised this ratio to 60.9%, with the high and extremely high potential areas accounting for 12.2% and 8.8% respectively. The high geothermal potential areas are mainly distributed in Decheng District, Lingcheng District and Pingyuan County in the north of the study area. Compared with the known well point distribution, the classification results of the two models are highly consistent, and the proportion of geothermal wells increases with the increase of potential grade, in which ViT-KAN accounts for 87.61% of geothermal wells in extremely high potential area, and the proportion of non-geothermal wells in medium and high potential area is significantly reduced. Thermal storage temperature, porosity and thermal storage thickness are the key factors affecting geothermal potential prediction, all of which are positive contributions. The research results can provide technical support for regional geothermal resources evaluation and target area optimization.