Machine Learning-Accelerated Multi-Objective Design of Fractured Geothermal Systems

Multi-objective optimization has burgeoned as a potent methodology for informed decision-making in enhanced geothermal systems, aiming to concurrently maximize economic yield, ensure enduring geothermal energy provision, and curtail carbon emissions. However, addressing a multitude of design parameters inherent in computationally intensive physics-driven simulations constitutes a formidable impediment for geothermal design optimization, as well as across a broad range of scientific and engineering domains. Here we report an Active Learning enhanced Evolutionary Multi-objective Optimization algorithm, integrated with hydrothermal simulations in fractured media, to enable efficient optimization of fractured geothermal systems using few model evaluations. We introduce probabilistic neural network as classifier to learns to predict the Pareto dominance relationship between candidate samples and reference samples, thereby facilitating the identification of promising but uncertain offspring solutions. We then use active learning strategy to conduct hypervolume based attention subspace search with surrogate model by iteratively infilling informative samples within local promising parameter subspace. We demonstrate its effectiveness by conducting extensive experimental tests of the integrated framework, including multi-objective benchmark functions, a fractured geothermal model and a large-scale enhanced geothermal system. Results demonstrate that the ALEMO approach achieves a remarkable reduction in required simulations, with a speed-up of 1-2 orders of magnitude (10-100 times faster) than traditional evolutionary methods, thereby enabling accelerated decision-making. Our method is poised to advance the state-of-the-art of renewable geothermal energy system and enable widespread application to accelerate the discovery of optimal designs for complex systems.