Transfer Learning for Flow Reconstruction Based on Multifidelity Data

Reduced-order modeling for multifidelity flow reconstruction offers increased accuracy while saving cost in data generation. The key to obtaining successful multifidelity models lies in properly capturing the correlation between low-fidelity and high-fidelity data. In this work, we propose to apply transfer learning to discover representative features that better correlate the multifidelity data to improve the accuracy in multifidelity flow reconstruction. Essentially, transfer learning facilitates the modeling task through transferring the knowledge learned in a related task, thus improving model performance in multifidelity problems. In particular, a typical class of transfer learning based on domain adaptation is introduced to discover domain-invariant features from the flow data of multiple sources. Two transfer learning frameworks via either the transfer component analysis or the geodesic flow kernel are established, providing different concepts to match transferred features between multifidelity data. Thereafter, the transferred features can be used as inputs to build the bridge function between low-fidelity and high-fidelity data for flow reconstruction. The proposed transfer learning methods are tested by various cases with increasing complexity, including heat convection, the Burgers equation, and transonic flows past a NACA0012 airfoil and an ONERA M6 wing. Advantages of the proposed transfer learning method to obtain better feature representations and to help construct more accurate multifidelity models for flow reconstruction are presented.