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In the present work, we propose a self-optimization wavelet-learning method(SO-W-LM) with high accuracy and efficiency to compute the equivalent nonlinearthermal conductivity of highly heterogeneous materials with randomlyhierarchical configurations. The randomly structural heterogeneity,temperature-dependent nonlinearity and material property uncertainty ofheterogeneous materials are considered within the proposed self-optimizationwavelet-learning framework. Firstly, meso- and micro-structural modeling ofrandom heterogeneous materials are achieved by the proposed computerrepresentation method, whose simulated hierarchical configurations haverelatively high volume ratio of material inclusions. Moreover,temperature-dependent nonlinearity and material property uncertainties ofrandom heterogeneous materials are modeled by a polynomial nonlinear model andWeibull probabilistic model, which can closely resemble actual materialproperties of heterogeneous materials. Secondly, an innovative stochasticthree-scale homogenized method (STSHM) is developed to compute the macroscopicnonlinear thermal conductivity of random heterogeneous materials. Backgroundmeshing and filling techniques are devised to extract geometry and materialfeatures of random heterogeneous materials for establishing material databases.Thirdly, high-dimensional and highly nonlinear material features of materialdatabases are preprocessed and reduced by wavelet decomposition technique. Theneural networks are further employed to excavate the predictive models fromdimension-reduced low-dimensional data.

Self-optimization wavelet-learning method for predicting nonlinear  thermal conductivity of highly heterogeneous materials with randomly  hierarchical configurations