Reduced Order Modeling of History-Dependent Plasticity via Neural Networks with Physically-Encoded Latent Spaces
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The computational expense of high-fidelity nonlinear simulations often precludes their use in iterative engineering workflows, such as structural topology optimization. This difficulty is primarily driven by path-dependent plasticity, where the necessity of tracking internal state variables makes standard surrogate modeling computationally heavy and physically opaque. To overcome these limitations, we propose the Spatiotemporal Physics-derived Internal Latent Space Network (SPILS-Net), a neural network-based ROM approach that prioritizes physical interpretability. Unlike conventional "black-box" recurrent surrogates that struggle with training costs, SPILS-Net adopts a "gray-box" strategy. It explicitly embeds physical history by projecting accumulated plastic strain into a PCA-reduced latent manifold. This structured latent space ensures that the neural network’s internal representations remain grounded in the underlying mechanics of the problem. To ensure robust temporal convergence, the model utilizes Gated Recurrent Units (GRU) trained via a "Teacher Forcing" protocol, effectively bypassing the gradient instabilities often encountered in path-dependent learning. We validate the framework using training data generated in FEniCSx. For practical deployment, the neural network surrogate is coupled with structural solvers using a non-iterative Dirichlet-Neumann scheme, enabling the direct prediction of converged interface forces. Results in structural mechanics benchmarks indicate that SPILS-Net provides a more stable alternative to standard LSTM architectures, demonstrating a significant acceleration in training alongside enhanced predictive accuracy.
