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Gaussian Processes (GP) are a powerful framework for modeling expensive black-box functions and have thus been adopted for various challenging modeling and optimization problems. In GP-based modeling, we typically default to a stationary covariance kernel to model the underlying function over the input domain, but many real-world applications, such as controls and cyber-physical system safety, often require modeling and optimization of functions that are locally stationary and globally non-stationary across the domain; using standard GPs with a stationary kernel often yields poor modeling performance in such scenarios. In this paper, we propose a novel modeling technique called Class-GP (Class Gaussian Process) to model a class of heterogeneous functions, i.e., non-stationary functions which can be divided into locally stationary functions over the partitions of input space with one active stationary function in each partition. We provide theoretical insights into the modeling power of Class-GP and demonstrate its benefits over standard modeling techniques via extensive empirical evaluations.