  In this paper, we employ Bayesian optimization to concurrently explore the
optimal values for both the shape parameter and the radius in the partition of
unity interpolation using radial basis functions. Bayesian optimization is a
probabilistic, iterative approach that models the error function through a
progressively self-updated Gaussian process. Meanwhile, the partition of unity
approach harnesses a meshfree method, allowing us to significantly reduce
computational expenses, particularly when considering a substantial number of
scattered data points. This reduction in computational cost is achieved by
decomposing the entire domain into several smaller subdomains, each of them
with a variable radius. We provide an estimation of the complexity of our
algorithm and carry out numerical experiments to illustrate the effectiveness
of our approach, dealing with test and real-world datasets.
