Implicitly physics-informed multi-fidelity physical field data fusion method based on Taylor modal decomposition

Ruofan Zhang, Xingchen Li, Wen Yao, Xiaohu Zheng, Ning Wang, Jialiang Sun

Abstract: Deep neural network (DNN)-based methods are becoming increasingly common in fusing multi-source and multi-physics heterogeneous (MSPH) data. However, these methods cannot achieve satisfactory transferable performance when the high-fidelity data is insufficient or the physical knowledge clashes with multi-source data due to the introduction of many approximate models involved in the physical governing equations. Besides, MSPH data exhibits characteristics of multi-resolution and multi-accuracy scales, uneven distribution, strong nonlinearity, and rich physical information, which result in significant challenges for the existing data fusion methods. Thus, to address the MSPH data fusion problem, this paper proposes a multi-fidelity physical field data (PFD) fusion method that combines DNN with the Taylor expansion theorem, i.e., implicitly physics-informed Taylor modal decomposition-based data fusion method. The proposed method extracts continuous partial differential information from numerical simulation and discrete precision information from measured sensors to obtain high-resolution and high-accuracy datasets. The decomposition and fusion of Taylor modes promote the incorporation of the physical Partial Differential Equations (PDEs) into the fusion process in an implicit way. Moreover, this paper presents an adaptively transferable training algorithm, which includes pre-training, fine-tuning, and adaptive-updating processes, achieving better performance of physical knowledge transfer from low fidelity to high fidelity. Three case studies are used to demonstrate the effectiveness and universality of the proposed method. The results show that the proposed method can effectively improve the accuracy of the MSPH data while ensuring the resolution and can be applied in multi-physics fields data fusion cases.