Introducing a microstructure-embedded autoencoder approach for reconstructing high-resolution solution field from reduced parametric space

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.