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.

翻译：本文采用贝叶斯优化方法，同步探索径向基函数单位分解插值中形状参数与半径的最优取值。贝叶斯优化作为一种概率迭代式方法，通过渐进自更新的高斯过程对误差函数进行建模。同时，单位分解法利用无网格技术，通过将整个计算域分解为若干半径可变的子域，显著降低了大量散乱数据点情形下的计算开销。我们给出了算法复杂度估计，并通过测试数据集与真实数据集开展数值实验，验证了所提方法的有效性。