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Predicting the process of porosity-based ductile damage in polycrystallinemetallic materials is an essential practical topic. Ductile damage and itsprecursors are represented by extreme values in stress and material statequantities, the spatial PDF of which are highly non-Gaussian with strong fattails. Traditional deterministic forecasts using physical models often fail tocapture the statistics of structural evolution during material deformation.This study proposes a data-driven statistical reduced-order modeling frameworkto provide a probabilistic forecast of the deformation process leading toporosity-based ductile damage, with uncertainty quantification. The frameworkstarts with computing the time evolution of the leading moments of specificstate variables from full-field polycrystal simulations. Then a sparse modelidentification algorithm based on causation entropy, including essentialphysical constraints, is used to discover the governing equations of thesemoments. An approximate solution of the time evolution of the PDF is obtainedfrom the predicted moments exploiting the maximum entropy principle. Numericalexperiments based on polycrystal realizations show that the model cancharacterize the time evolution of the non-Gaussian PDF of the von Mises stressand quantify the probability of extreme events. The learning process alsoreveals that the mean stress interacts with higher-order moments and extremeevents in a strongly nonlinear and multiplicative fashion. In addition, thecalibrated moment equations provide a reasonably accurate forecast when appliedto the realizations outside the training data set, indicating the robustness ofthe model and the skill for extrapolation. Finally, an information-basedmeasurement shows that the leading four moments are sufficient to characterizethe crucial non-Gaussian features throughout the entire deformation history.

Data-Driven Statistical Reduced-Order Modeling and Quantification of Polycrystal Mechanics Leading to Porosity-Based Ductile Damage