A new approach for data-driven surrogate modelling applied in highly nonlinear engineering functions

A data-driven surrogate mimics the behavior of a black-box simulation model using selected input-output data points. Highly nonlinear models challenge many surrogate techniques in engineering design. This study proposes a reliable surrogate for training small-scale problems (two or three input variables). A combination of local and semi-global interpolators is introduced to approximate responses for new sample points in the design space. The local predictor uses a linear combination of two adjacent points, while the semi-global predictor employs K-means clustering, averaging samples in each cluster, and weighting clusters based on Euclidean distances. The trade-off between predictors is optimized using jackknife resampling error minimized via Genetic Algorithm (GA). Performance comparisons with Kriging, Radial Basis Function (RBF), and Support Vector Machine (SVM) confirm the proposed surrogate's accuracy and robustness using five benchmark functions and two engineering problems. Results demonstrate superior interpolation of nonlinear functions with reduced error and improved robustness.