Machine Learning-based Domain Decomposition Approach via the Predefined Lagrange Multipliers
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Domain decomposition approach has been widely utilized for expedited design and numerical simulation, by significantly reducing the computational time for large-size situation. As construction of the surrogate models based on the high-fidelity simulation generally requires a substantial amount of storage and extensive training result, it will lead to extravagant computational and memory cost. In this abstract, a machine learning-based non-overlapping domain decomposition framework is proposed to reduce the required training set by exploiting interface variables among the decomposed subdomains. Specifically, Lagrange multipliers defined on the interface will be predicted by the machine learning technique. The predicted Lagrange multipliers will then be employed to compute the physical response of the adjoint subdomains. Such framework will be constructed based on the dual-primal finite element tearing and interconnecting (FETI-DP). The proposed method will be compared against the original FETI-DP and full degree of freedom representation to demonstrate its accuracy and efficiency.
