In this study, we develop a novel multi-fidelity deep learning approach that
transforms low-fidelity solution maps into high-fidelity ones by incorporating
parametric space information into a standard autoencoder architecture. It is
shown that, due to the integration of parametric space data, this method
requires significantly less training data to achieve effective performance in
predicting high-fidelity solution from the low-fidelity one. In this study, our
focus is on a 2D steady-state heat transfer analysis in highly heterogeneous
materials microstructure, where the spatial distribution of heat conductivity
coefficients for two distinct materials is condensed. Subsequently, the
boundary value problem is solved on the coarsest grid using a pre-trained
physics-informed neural operator network. Afterward, the calculated
low-fidelity result is upscaled using the newly designed enhanced autoencoder.
The novelty of the developed enhanced autoencoder lies in the concatenation of
heat conductivity maps of different resolutions to the decoder segment in
distinct steps. We then compare the outcomes of developed algorithm with the
corresponding finite element results, standard U-Net architecture as well as
other upscaling approaches such as interpolation functions of varying orders
and feedforward neural networks (FFNN). The analysis of the results based on
the new approach demonstrates superior performance compared to other approaches
in terms of computational cost and error on the test cases. Therefore, as a
potential supplement to neural operators networks, our architecture upscales
low-fidelity solutions to high-fidelity ones while preserving critical details
that are often lost in conventional upscaling methods, especially at sharp
interfaces, such as those encountered with interpolation methods.

研究中开发了一种新颖的多保真度深度学习方法，通过将参数空间信息纳入标准自动编码器体系结构中，将低保真度解决方案图转换为高保真度解决方案图，并表明由于参数空间数据的整合，该方法要求显著较少的训练数据来实现从低保真度到高保真度的有效性能。