Forecasting geothermal temperature in western Yemen with Bayesian-optimized machine learning regression models

Geothermal energy is a sustainable resource for power generation, particularly in Yemen. Efficient utilization necessitates accurate forecasting of subsurface temperatures, which is challenging with conventional methods. This research leverages machine learning (ML) to optimize geothermal temperature forecasting in Yemen's western region. The data set, collected from 108 geothermal wells, was divided into two sets: set 1 with 1402 data points and set 2 with 995 data points. Feature engineering prepared the data for model training. We evaluated a suite of machine learning regression models, from simple linear regression (SLR) to multi-layer perceptron (MLP). Hyperparameter tuning using Bayesian optimization (BO) was selected as the optimization process to boost model accuracy and performance. The MLP model outperformed others, achieving high R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {R}<^>{2}$$\end{document} values and low error values across all metrics after BO. Specifically, MLP achieved R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {R}<^>{2}$$\end{document} of 0.999, with MAE of 0.218, RMSE of 0.285, RAE of 4.071%, and RRSE of 4.011%. BO significantly upgraded the Gaussian process model, achieving an R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {R}<^>{2}$$\end{document} of 0.996, a minimum MAE of 0.283, RMSE of 0.575, RAE of 5.453%, and RRSE of 8.717%. The models demonstrated robust generalization capabilities with high R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\text {R}<^>{2}$$\end{document} values and low error metrics (MAE and RMSE) across all sets. This study highlights the potential of enhanced ML techniques and the novel BO in optimizing geothermal energy resource exploitation, contributing significantly to renewable energy research and development.