High-Dimensional Nonlinear Multi-Fidelity Model with Gradient-Free Active Subspace Method (Communications in Computational Physics, 2020)
In scientific and engineering applications, often sufficient low-cost low-fidelity data is available while only a small fractional of high-fidelity data is accessible. The multi-fidelity model integrates a large set of low-cost but biased low-fidelitydatasets with a small set of precise but high-cost high-fidelity data to make an accurateinference of quantities of interest. Under many circumstances, the number of modelinput dimensions is often high in real applications. To simplify the model, dimensionreduction is often used. The gradient-free active subspace is employed in this researchfor dimension reduction. In this work, a novel predictive model for high-dimensionalnonlinear problems by integrating the nonlinear multi-fidelity Gaussian progress regression and the gradient-free active subspace method is put forward. Numerical results demonstrated that the proposed approach can not only perform effective dimension reduction on the original data but also obtain accurate prediction results thanksto the effective dimension reduction procedure.
Keywords: Gaussian process regression; dimension reduction; multi-fidelity model; active subspace; machine learning.