Bridging Physical Interpretability and Data-Driven Efficiency for History-Dependent ROM via SPILS-Net
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High-fidelity numerical simulations are essential for modern engineering, yet their computational cost remains a barrier for iterative tasks like topology optimization. This challenge is compounded when modeling history-dependent plasticity, as internal state variables make traditional surrogate modeling difficult. While recent frameworks like Finite Element Method Integrated Networks (FEMIN) use recurrent architectures to capture these behaviors, they often rely on "black box" systems that are expensive to train and lack physical interpretability. This paper presents the Spatiotemporal Physics-derived Internal Latent Space Network (SPILS-Net). To specifically address the challenges of history-dependent ROM, SPILS-Net maps accumulated plastic strain onto a PCA-reduced manifold to explicitly propagate history, ensuring the internal state remains physically meaningful and computationally efficient. The custom architecture utilizes Gated Recurrent Units (GRU) to manage temporal evolution but introduces a "Teacher Forcing" strategy during training to bypass the instabilities of traditional Backpropagation Through Time. Training data is generated within the FEniCSx environment, and the surrogate is integrated into structural solvers through a non-iterative Dirichlet-Neumann coupling to predict converged interface forces directly. Preliminary benchmarks in structural mechanics show that SPILS-Net demonstrates a multi-fold increase in computational efficiency compared to standard recurrent architectures while maintaining comparable accuracy.