Adaptive Machine Learning-Enhanced Optimization for Scalar Field Reconstruction

In this article, we propose a novel framework for solving complex optimization problems using a hybrid approach that combines machine learning (ML) with a metaheuristic algorithm. The proposed framework, called ML-enhanced, leverages the strengths of both approaches to reduce the number of function evaluations required for optimization. We demonstrate the effectiveness of our framework through experiments on two challenging problems: artificial inflation device (AID) and switched fuel ratio (SFR).
The article begins by providing context about the PSO algorithm, which is widely used in optimization problems, but has limited ability to handle complex searches. To address this limitation, we introduce the ML-enhanced framework, which combines the PSO algorithm with an ML model that can learn the underlying relationship between the search space and the objective function. By doing so, the ML model can approximate the objective function, reducing the number of function evaluations required by the PSO algorithm.
We evaluate the performance of our proposed framework using two real-world optimization problems: AID and SFR. Our results show that the ML-enhanced framework achieves better accuracy and efficiency compared to the traditional PSO algorithm. Specifically, we observe a 25% reduction in the number of function evaluations required for the AID problem, and a 30% reduction for the SFR problem.
To further analyze the performance of our proposed framework, we perform an extensive hyperparameter analysis. We identify the optimal values for each hyperparameter and demonstrate that the ML-enhanced framework can adapt to different problem sizes and complexities.
Finally, we discuss the advantages and limitations of our proposed framework and highlight potential avenues for future research. Our findings suggest that the ML-enhanced framework has the potential to significantly improve the efficiency and accuracy of optimization algorithms in various fields, including climate and combustion simulations. However, there are still some limitations to be addressed, such as the need for high-quality training data and the potential impact of hyperparameter tuning on the performance of the ML model.
In summary, this article proposes a novel framework that combines machine learning with a metaheuristic algorithm to solve complex optimization problems more efficiently. Our proposed framework, called ML-enhanced, has been tested on two real-world problems and shown to achieve better accuracy and efficiency compared to traditional optimization algorithms. The extensive hyperparameter analysis and thorough discussion of the advantages and limitations provide insights into the potential applications and areas for future research in this promising field.