A multiscale analysis-assisted two-stage reduced-order deep learning approach for effective thermal conductivity of arbitrary contrast heterogeneous materials

Effective thermal conductivity (ETC) is an important property of heterogeneous materials in many thermal management applications. Recently, there is increasing interest to establish the structure-property linkage through machine learning methods. One limitation is that their prediction accuracy is highly dependent on the extremely large space of descriptors of heterogeneous materials due to complex microstructure. Besides, they are also based on a large quantity of data samples, especially for the high contrast heterogeneous materials due to the strongly nonlinear relationship between ETC and volume fraction ratios. In this study, a novel two-stage reduced-order deep learning approach assisted multiscale analysis is proposed to predict the ETC of arbitrary contrast heterogeneous materials with complex microstructure. The key point of the approach is that a two-stage reduced-order strategy is proposed to extract the sample features from any data sample and the feature samples from the database by deep learning approach. The high-fidelity dataset relating the microstructural images of heterogeneous materials with different volume fractions to their corresponding ETC is generated by the asymptotic homogenization method assisted with finite element algorithm. The multiscalebased database and the two-stage reduced-order learning strategy ease the training of neural networks, and enable us to efficiently build more simple networks for approximating mappings of very high complexity. 2D and 3D interpenetrating phase composites were employed as the examples to illustrate the method. The trained network is validated to be able to establish the structure-property linkage accurately and efficiently. Not limited to interpenetrating phase composites, the proposed method can be further extended to predict ETC of other heterogeneous materials.