An Information-theoretic Multiscale Framework with Applications to Polycrystalline Materials

We considered the feasibility of utilizing High Dimensional Model Representation (HDMR) technique in the stochastic space to represent the model output as a finite hierarchical correlated function expansion in terms of the stochastic inputs starting from lower-order to higher-order component functions. HDMR is efficient at capturing the high-dimensional input-output relationship such that the behavior for many physical systems can be modeled only by the first few lower-order terms. An adaptive version of HDMR is developed to automatically detect the important dimensions and construct higher-order terms only as a function of the important dimensions. In this work, we also incorporate the newly developed adaptive sparse grid collocation (ASGC) method into HDMR to solve the resulting sub-problems. The efficiency of the proposed method is examined by comparing with Monte Carlo (MC) simulation. Finally, we developed a unique data-driven strategy to encode the limited information on initial texture in deformation processes and represent it in a finite-dimensional framework. We have developed the ability to produce the probabilistic distribution of the macro-scale properties of the material subjected to a specific process induced by the uncertainty in initial texture.