Gaussian Process Controlled B-Spline Surface

We propose a Gaussian process controlled B-spline surface (GPBSS), which integrates the flexibility of B-spline basis functions into the probabilistic framework of Gaussian processes. By leveraging the sparsity inherent in B-spline bases, GPBSS achieves a linear time complexity, making it particularly effective for large-scale data sets in low-dimensional spaces. Compared with current benchmark approximations of the standard Kriging model, GPBSS offers a unique balance between computational efficiency and prediction accuracy. Furthermore, we extend the application of the GPBSS model to Bayesian optimization, enabling efficient optimization of black box functions. To validate the performance of GPBSS, we conduct a regression study on four large-scale data sets and an optimization study on three complex objective functions. The results demonstrate that our proposed model not only significantly enhances computational efficiency but also excellently balances its prediction accuracy. Its favorable tradeoff makes GPBSS a valuable tool for data-intensive regression and optimization tasks in low-dimensional scenarios such as medical imaging, geospatial analysis, and additive manufacturing,