Integrated multi-physics simulation and machine learning-based multi-objective optimization for enhanced geothermal system heat extraction performance

Geothermal energy represents a pervasive, environmentally friendly, and plentiful form of renewable energy. Optimizing engineering parameters and understanding the factors that influence heat extraction performance are critical for the stable and efficient operation of enhanced geothermal systems (EGS). This study investigates the evolution of heat extraction performance under varying engineering parameters using a thermo-hydraulic-mechanical multi-physics coupling model combined with finite element numerical simulations. Based on these simulations, a backpropagation (BP) neural network was optimized using a Newton-Raphson-based optimizer (NRBO-BP), enabling the construction of a multi-input, multi-output prediction model for EGS heat extraction performance. The NRBO-BP prediction model was then employed as an implicit surrogate within a multi-objective optimization framework. By integrating the multi-objective seagull optimization algorithm with the Entropy Weight-TOPSIS method, a comprehensive decision-making methodology was established to optimize heat extraction performance. This approach allows for the simultaneous adjustment of multiple parameters under diverse operational constraints. The results demonstrate that the NRBO-optimized model achieves significantly higher predictive accuracy than the conventional BP neural network. Following multi-objective optimization of the engineering parameters, the geothermal system now extends its operational lifespan by over 10 years and significantly reduces the injection-production pressure differential by 76.4%, thereby improving heat extraction efficiency and overall system stability. These findings establish both a theoretical foundation as well as a practical methodology to promoting the sustainable and reliable advancement of geothermal energy. This study establishes a novel multi-input, multi-output prediction model for heat extraction performance and introduces a hybrid optimization method, offering valuable insights for future EGS applications.