Practical sparse data-driven constitutive modeling via transfer learning in physics-encoded neural networks

Data-driven constitutive models, owing to their inherent flexibility, can outperform traditional plasticity-based models in certain aspects. When calibrating these models, ensuring adherence to fundamental mechanical principles allows the calibrated models, referred to as physics-encoded neural networks (PeNNs), to be effectively integrated into finite element method (FEM) software for boundary value problem simulations. However, calibration challenges arise when only limited data are available. Addressing this issue, this study employs transfer learning. Synthetic labeled data, derived from traditional constitutive models were used to pre-train PeNNs. Subsequently, these pre-trained PeNNs are fine-tuned using implicitly labeled data from high-fidelity experimental records. The fine-tuned models are integrated into FEM software as user materials to conduct extensive drained and undrained triaxial test simulations. An analysis of the simulation results highlights the impact of the available volume of experimental data, the quantity of synthetic data, and key configurations in the fine-tuning process, such as the architecture of the fine-tuning model, frozen parameters, and batch size. Results indicate that through robust PeNN models and meticulous modeling, transfer learning can establish a data-driven constitutive model with limited experimental records, achieving superior simulation performance compared to the synthetic model alone. This underscores the potential of combining cost-effective synthetic and experimental data to advance constitutive modeling.