An Auto-regressive Kriging Model for Problems with Multiple Outputs

This paper proposes an auto-regressive Kriging (Krig-AR) model to enhance the accuracy of multi-output surrogate modeling while minimizing computational overhead. Traditional Kriging models handle multiple outputs independently, ignoring inherent inter-output correlations crucial for engineering applications like multi-objective optimization. To address this, Krig-AR sequentially models each output by augmenting input dimensions with predictions from prior outputs. A composite correlation function captures dependencies between inputs and outputs. The model leverages the infinite-width Bayesian neural network (IBNN) correlation function, which outperforms Gaussian correlation in high-dimensional input spaces due to its hyperparameter efficiency. Validation on a synthetic problem and an airfoil aerodynamic performance case (lift/drag prediction) demonstrates that Krig-AR significantly improves accuracy for correlated outputs compared to independent Kriging with Gaussian or IBNN correlation. Results confirm superior accuracy, particularly for downstream outputs.