Gradient Descent-based D-optimal Design for the Least-Squares Polynomial Approximation
For computational modelers needing efficient surrogate models, this method offers a novel approach to reduce approximation error, though results are demonstrated only on polynomial approximation problems.
The paper proposes a gradient descent-based D-optimal design method for sampling input parameters in least-squares polynomial approximation, achieving lower approximation errors compared to LHS, Sobol sequences, and Maxvol sampling in numerical experiments.
In this work, we propose a novel sampling method for Design of Experiments. This method allows to sample such input values of the parameters of a computational model for which the constructed surrogate model will have the least possible approximation error. High efficiency of the proposed method is demonstrated by its comparison with other sampling techniques (LHS, Sobol' sequence sampling, and Maxvol sampling) on the problem of least-squares polynomial approximation. Also, numerical experiments for the Lebesgue constant growth for the points sampled by the proposed method are carried out.