Insufficient data quantity cannot guarantee good quality for constructing a surrogate, while Garud et al. report that simply increasing the data quantity cannot lead to better performance of a surrogate. Thus, the quality of surrogates should rely on both -data quantity and quality. To reduce the time for data generation, the first objective is to obtain good-enough surrogates with the minimum amount of data. There are two types of sampling methods: one-shot and sequential (adaptive) methods. The former method samples the design space uniformly in one go and then builds a surrogate, while the latter samples data in batch and refine the surrogate iteratively. The one-shot is straightforward but may result in under/over-sampling, where either poor regression or inefficiency can occur. In recent years, the sequential methods tend to be popular because they are reported to better balance the regression performance and efficiency. However, over-sampling is still hard to avoid by a typical sequential method. To demonstrate this, we still use the example of a PSA process. Mean squared errors (MSE) is employed to evaluate the regression performance. The data is sequentially sampled in a space-filling method, which is stochastic. A stochastic method has anytime behavior, where sampling can be stopped at any time. We plot the fitting performance against time to observe the termination condition as shown in Figure . We divide the sequential sampling as two equal parts based on the number of data points (approximately equivalent to time, because the time for surrogate training can be neglected compared to data generation as shown in Figure ). The plot indicates that regression improvement in the first half is significantly greater than that in the second half.