Design Space Exploration via Gaussian Process Regression and Alpha Shape Visualization

This study introduces a novel methodology that combines Gaussian process regression (GPR) with alpha shape design space reconstruction to visualize multi-dimensional design spaces. The proposed GPR surrogate approach incorporates a kernel optimization step, employing a greedy tree search strategy to identify the optimal combinatorial kernel from a selection of base kernels. This approach efficiently evaluates design spaces around specific points of interest, enabling alpha shape reconstruction. The methodology's adaptability is demonstrated through its application to both lower-dimensional (2D and 3D) cases and more complex, higher-dimensional systems (up to 7D), showcasing its scalability and versatility. Its effectiveness is further validated by its ability to generate accurate surrogate models from limited data. Overall, this study presents a robust framework that leverages GPR surrogate modeling and alpha shape reconstruction to facilitate design space evaluation in complex, multidimensional engineering problems.