Machine-learning-accelerated multi-objective design of fractured geothermal systems

Abstract

<h2>Summary</h2> 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 to 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 (ALEMO) algorithm, integrated with hydrothermal simulations in fractured media, to enable efficient optimization of fractured geothermal systems using a few model evaluations. We introduce a probabilistic neural network as a classifier to learn 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 an active learning strategy to conduct a hypervolume-based attention subspace search with a surrogate model by iteratively infilling informative samples within local promising parameter subspace. We demonstrate its effectiveness by conducting extensive experimental tests on the integrated framework, including multi-objective benchmark functions, a fractured geothermal model, and a large-scale enhanced geothermal system. The 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) compared to traditional evolutionary methods, thereby enabling accelerated decision-making. Our method is poised to advance the state of the art of renewable geothermal energy systems and enable widespread application to accelerate the discovery of optimal designs for complex systems.

Topics & Concepts