Accelerated multiscale data-driven finite element analysis using mean-field homogenization method with knowledge transfer

초록

This study presents an accelerated data-driven multiscale finite element framework that combines mean-field homogenization, proper orthogonal decomposition, and transfer learning to achieve accurate and computationally efficient multiscale structural analysis. The proposed approach addresses the prohibitive offline cost in classical multiscale finite element analysis and data sparsity inherent in data-driven multiscale methods by adopting a multi-fidelity learning strategy. A large, low-cost dataset generated via mean-field homogenization was first used to pre-train a neural network in a reduced proper orthogonal decomposition space, capturing global constitutive trends. Subsequently, a limited set of high-fidelity finite element analysis data was employed to fine-tune the model through transfer learning, effectively correcting mean-field homogenization induced modeling errors. Unlike mean-field homogenization approaches that provide only homogenized responses, the proposed framework enables the reconstruction of detailed microscopic stress fields by predicting proper orthogonal decomposition coefficients associated with finite element analysis modes. The resulting proposed model is integrated into a data-driven computational mechanics framework, replacing repeated microscopic representative volume element analyses during online computation. Extensive numerical studies demonstrate that the proposed method achieves accuracy comparable to classical multiscale finite element analysis while reducing total computational cost by more than half. Moreover, the framework exhibits strong robustness and generalization capability, providing reliable predictions even beyond the finite element analysis training data range. These results indicate that the proposed framework offers an efficient and scalable solution for high-fidelity multiscale analysis of heterogeneous materials.

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