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.

Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems

Surrogate-assisted evolutionary algorithms have been widely developed to solve complex and computationally expensive multi-objective optimization problems in recent years. However, when dealing with high-dimensional optimization problems, the performance of these surrogate-assisted multi-objective evolutionary algorithms deteriorate drastically. In this work, a novel Classifier-assisted rank-based learning and Local Model based multi-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensional expensive multi-objective optimization problems. The proposed algorithm consists of three parts: classifier-assisted rank-based learning, hypervolume-based non-dominated search, and local search in the relatively sparse objective space. Specifically, a probabilistic neural network is built as classifier to divide the offspring into a number of ranks. The offspring in different ranks uses rank-based learning strategy to generate more promising and informative candidates for real function evaluations. Then, radial basis function networks are built as surrogates to approximate the objective functions. After searching non-dominated solutions assisted by the surrogate model, the candidates with higher hypervolume improvement are selected for real evaluations. Subsequently, in order to maintain the diversity of solutions, the most uncertain sample point from the non-dominated solutions measured by the crowding distance is selected as the guided parent to further infill in the uncertain region of the front. The experimental results of benchmark problems and a real-world application on geothermal reservoir heat extraction optimization demonstrate that the proposed algorithm shows superior performance compared with the state-of-the-art surrogate-assisted multi-objective evolutionary algorithms. The source code for this work is available at https://github.com/JellyChen7/CLMEA.

Surrogate-assisted level-based learning evolutionary search for heat extraction optimization of enhanced geothermal system

An enhanced geothermal system is essential to provide sustainable and long-term geothermal energy supplies and reduce carbon emissions. Optimal well-control scheme for effective heat extraction and improved heat sweep efficiency plays a significant role in geothermal development. However, the optimization performance of most existing optimization algorithms deteriorates as dimension increases. To solve this issue, a novel surrogate-assisted level-based learning evolutionary search algorithm (SLLES) is proposed for heat extraction optimization of enhanced geothermal system. SLLES consists of classifier-assisted level-based learning pre-screen part and local evolutionary search part. The cooperation of the two parts has realized the balance between the exploration and exploitation during the optimization process. After iteratively sampling from the design space, the robustness and effectiveness of the algorithm are proven to be improved significantly. To the best of our knowledge, the proposed algorithm holds state-of-the-art simulation-involved optimization framework. Comparative experiments have been conducted on benchmark functions, a two-dimensional fractured reservoir and a three-dimensional enhanced geothermal system. The proposed algorithm outperforms other five state-of-the-art surrogate-assisted algorithms on all selected benchmark functions. The results on the two heat extraction cases also demonstrate that SLLES can achieve superior optimization performance compared with traditional evolutionary algorithm and other surrogate-assisted algorithms. This work lays a solid basis for efficient geothermal extraction of enhanced geothermal system and sheds light on the model management strategies of data-driven optimization in the areas of energy exploitation.