An Adaptive Non-Intrusive Multi-Fidelity Reduced Basis Method for Parameterized Partial Differential Equations

An adaptive non-intrusive multi-fidelity reduced basis method for parameterized partial differential equations is developed. Based on snapshots with different fidelity, the method reduces the number of high-fidelity snapshots in the regression model training and improves the accuracy of reduced-order model. One can employ the reduced-order model built on the low-fidelity data to adaptively identify the important parameter 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 the singular value decomposition of the low-fidelity snapshot matrix. Coefficients of such multi-fidelity reduced basis are determined by projecting low-fidelity snapshots on the low-fidelity reduced basis and using the Gaussian process regression. The projection method is more accurate than the regression method, but it requires low-fidelity snapshots. The regression method trains the Gaussian process regression only once but with slightly lower accuracy. Numerical tests show that the proposed multi-fidelity method can improve the accuracy and efficiency of reduced-order models.