A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

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Bayesian Model and Dimension Reduction for Uncertainty Propagation: Applications in Random Media (2017, background): “Furthermore, only a small portion of this work has been directed to stochastic/probabilistic multiscale problems [14] and even less, to strategies that would be applicable to high-dimensional, non-Gaussian uncertainties encountered in materials problems [69, 48].”
An iterative Bayesian filtering framework for fast and automated calibration of DEM models (2019, background): “For example, implementing a heterogeneous distribution of material properties in multiscale simulations is a typical approach to identify the sources of aleatory uncertainty [77].”
A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database (2019, methodology): “3 obtaining data-enhanced physical models [34,35], online updating dynamical system in a manner similar to data assimilation [36], or constructing reduced-order model [25,37–40].”