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This paper introduces an extended tensor decomposition (XTD) method for modelreduction. The proposed method is based on a sparse non-separated enrichment tothe conventional tensor decomposition, which is expected to improve theapproximation accuracy and the reducibility (compressibility) in highlynonlinear and singular cases. The proposed XTD method can be a powerful toolfor solving nonlinear space-time parametric problems. The method has beensuccessfully applied to parametric elastic-plastic problems and real timeadditive manufacturing residual stress predictions with uncertaintyquantification. Furthermore, a combined XTD-SCA (self-consistent clusteringanalysis) strategy has been presented for multi-scale material modeling, whichenables real time multi-scale multi-parametric simulations. The efficiency ofthe method is demonstrated with comparison to finite element analysis. Theproposed method enables a novel framework for fast manufacturing and materialdesign with uncertainties.

Extended tensor decomposition model reduction methods: training, prediction, and design under uncertainty