In this paper, Bayesian optimisation is used to simultaneously search the optimal values of the shape parameter and the radius in radial basis function partition of unity interpolation problem. It is a probabilistic iterative approach that models the error function with a step-by-step self-updated Gaussian process, whereas partition of unity leverages a mesh-free method that allows us to reduce cost-intensive computations when the number of scattered data is very large, as the entire domain is decomposed into several smaller subdomains of variable radius. Numerical experiments on the scattered data interpolation problem show that the combination of these two tools sharply reduces the search time with respect to other techniques such as the leave one out cross validation.

翻译：本文采用贝叶斯优化方法同步搜索径向基函数单位分解插值问题中形状参数与半径的最优取值。该概率迭代方法通过逐步自更新的高斯过程对误差函数进行建模，而单位分解技术则利用无网格方法，将整个计算域分解为多个可变半径的子域，从而在海量散乱数据场景下显著降低高成本计算量。针对散乱数据插值问题的数值实验表明，相较于留一交叉验证等传统技术，这两种工具的结合可大幅缩减搜索耗时。