An adaptive non-intrusive multi-fidelity reduced basis method for parameterized partial differential equations

An adaptive non-intrusive multi-fidelity reduced basis method for parame-terized partial differential equations is developed. Based on snapshots with differentfidelity, the method reduces the number of high-fidelity snapshots in the regressionmodel training and improves the accuracy of reduced-order model. One can employ thereduced-order model built on the low-fidelity data to adaptively identify the importantparameter values for the high-fidelity evaluations under a given tolerance. The multi-fidelity reduced basis is constructed based on the high-fidelity snapshot matrix and thesingular value decomposition of the low-fidelity snapshot matrix. Coefficients of suchmulti-fidelity reduced basis are determined by projecting low-fidelity snapshots on thelow-fidelity reduced basis and using the Gaussian process regression. The projectionmethod is more accurate than the regression method, but it requires low-fidelity snap-shots. The regression method trains the Gaussian process regression only once but withslightly lower accuracy. Numerical tests show that the proposed multi-fidelity methodcan improve the accuracy and efficiency of reduced-order models.

East Asian Journal on Applied Mathematics