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In this paper, we employ Bayesian optimization to concurrently explore theoptimal values for both the shape parameter and the radius in the partition ofunity interpolation using radial basis functions. Bayesian optimization is aprobabilistic, iterative approach that models the error function through aprogressively self-updated Gaussian process. Meanwhile, the partition of unityapproach harnesses a meshfree method, allowing us to significantly reducecomputational expenses, particularly when considering a substantial number ofscattered data points. This reduction in computational cost is achieved bydecomposing the entire domain into several smaller subdomains, each of themwith a variable radius. We provide an estimation of the complexity of ouralgorithm and carry out numerical experiments to illustrate the effectivenessof our approach, dealing with test and real-world datasets.

Parameter Tuning in the Radial Kernel-Based Partition of Unity Method by Bayesian Optimization