This paper introduces an extended tensor decomposition (XTD) method for model reduction. The proposed method is based on a sparse non-separated enrichment to the conventional tensor decomposition, which is expected to improve the approximation accuracy and the reducibility (compressibility) in highly nonlinear and singular cases. The proposed XTD method can be a powerful tool for solving nonlinear space-time parametric problems. The method has been successfully applied to parametric elastic-plastic problems and real time additive manufacturing residual stress predictions with uncertainty quantification. Furthermore, a combined XTD-SCA (self-consistent clustering analysis) strategy has been presented for multi-scale material modeling, which enables real time multi-scale multi-parametric simulations. The efficiency of the method is demonstrated with comparison to finite element analysis. The proposed method enables a novel framework for fast manufacturing and material design with uncertainties.

翻译：本文提出了一种用于模型降阶的扩展张量分解（XTD）方法。该方法基于对传统张量分解进行稀疏非分离富集，有望在高度非线性和奇异情形下提高逼近精度与可约性（可压缩性）。所提出的XTD方法可成为求解非线性时空参数化问题的有力工具。该方法已成功应用于参数化弹塑性问题及含不确定性量化的实时增材制造残余应力预测。此外，本文还提出了XTD-SCA（自洽聚类分析）联合策略用于多尺度材料建模，能够实现实时多尺度多参数模拟。通过与有限元分析的对比，验证了该方法的有效性。所提方法为含不确定性的快速制造与材料设计提供了新型框架。