We present a novel sequential experimental design framework that combines the interpretability of classical response surface

methodology with the adaptability of Bayesian optimization. At each iteration, a second-order polynomial surrogate model

is refitted and the next experiment is selected using a variance-weighted curvature (VWC) acquisition function that targets

locations where the surrogate is uncertain and/or strongly curved. Sampling in these information-rich regions can improve

global model fidelity while still revealing optima. Through three benchmark problems—including a five-dimensional sparse

quadratic and a non-quadratic surface—the VWC criterion achieves one to three orders of magnitude lower prediction error

than Gaussian process-based Bayesian optimization while requiring significantly less computation. The proposed framework

is fast, interpretable, and readily scalable, making it well suited to data-intensive experimentation in chemical engineering

and related fields.