A wavelet-based learning approach assisted multiscale analysis for estimating the effective thermal conductivities of particulate composites

Multiscale modeling for estimating the effective thermal conductivities of particulate composites with complex microstructures remains a challenging problem. This is mainly due to the non-linear physics, the high-dimensional property, and the fact that many repeated evaluations of the multiscale model are often required. In this study, we develop an innovative wavelet-based learning approach assisted multiscale analysis to predict the effective thermal conductivities of particulate composites with heterogeneous conductivity. This novel method combines respective advantages of multiscale modeling, wavelet transform and artificial neural network (ANN) together. By virtue of asymptotic homogenization method (AHM), a multiscale model is proposed for establishment of the material database with high-dimensional and highly-complex mappings. The multiscale material database and the wavelet-based learning strategy ease the training of neural networks, and enable us to efficiently build more simple networks that have an essentially increasing capacity and resisting noise for approximating mappings of very high complexity. Moreover, it should be noted that the wavelet-based learning strategy can not only extract important data features from material database, but also achieve a great reduction in input data of neural networks for resolving the great difficulty due to taking a large data set from the entire material database and ensuring the successful training the neural networks. The numerical experiments performed using periodic and random particulate composite models in 2D and 3D cases illustrate the outstanding performance of the integrated method. The obtained results indicate that the wavelet-based learning approach is a robust method for estimating the effective thermal conductivities with different heterogeneity patterns. The proposed method can significantly reduce the computational time, and can be further extended to predict effective mechanical properties of particulate composites.