Extended Low-Rank Approximation Accelerates Learning of Elastic Response in Heterogeneous Materials

Abstract: Predicting how the microstructure governs the mechanical response of heterogeneous materials is essential for optimizing design and performance. Yet this task remains difficult due to the complex, high dimensional nature of microstructural features. Relying on physics based simulations to probe the microstructural space is computationally prohibitive. This motivates the development of computational tools to efficiently learn structure property linkages governing mechanical behavior. While contemporary data driven approaches offer new possibilities, they often require large datasets. To address this challenge, this work presents the Extended Low Rank Approximation (xLRA), a framework that employs canonical polyadic tensor decomposition. It efficiently maps high dimensional microstructural information to the local elastic response by adaptively incorporating higher rank terms. xLRA accurately predicts the local elastic strain fields in porous microstructures, requiring a maximum rank of only 4. The compact formulation of xLRA achieves accurate predictions when trained on just 5% of the dataset, demonstrating significant data efficiency. Moreover, xLRA proves transferability by delivering results across representative material systems, including two phase composites and single and dual phase polycrystals. Despite being compact, xLRA retains essential microstructural details, enabling accurate predictions on unseen microstructures. Benchmarking shows that xLRA outperforms contemporary methods in predictive accuracy, generalizability, and computational efficiency, while requiring 6 orders of magnitude fewer floating point operations. In summary, xLRA provides an efficient framework for predicting the elastic response from microstructures, enabling scalable mapping of structure property linkages.