Efficient Global Surrogate Modeling Based on Multi-Layer Sampling

Global surrogate modeling aims to build surrogate model with high accuracy in the whole design domain. A major challenge to achieve this objective is how to reduce the number of function evaluations to the original computer simulation model. To date, the most widely used approach for global surrogate modeling is the adaptive surrogate modeling method. It starts with an initial surrogate model, which is then refined adaptively using the mean square error (MSE) or maximizing the minimum distance criteria. It is observed that current methods may not be able to effectively construct a global surrogate model when the underlying black box function is highly nonlinear in only certain regions. A new surrogate modeling method which can allocate more training points in regions with high nonlinearity is needed to overcome this challenge. This article proposes an efficient global surrogate modeling method based on a multi-layer sampling scheme. An initial surrogate model is constructed first with a small group of training points. After that, samples of input variables are generated in multiple layers over the design domain. The generated samples have the space-filling property over the design domain and across layers. From the generated samples, new training point and candidate training points are identified in different layers by directly minimizing the prediction bias of the surrogate model. This enables us to improve the accuracy of surrogate model prediction more effectively than current available methods. Several mathematical examples and a nonlinear vibratory system are used to demonstrate the effectiveness of the proposed global surrogate modeling method. The results show that the proposed method performs better than the most widely used variance minimization (VM) method.