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

## TL;DR

This paper introduces a method to build better soil models using limited data by combining synthetic and real-world data through transfer learning in physics-based neural networks.

## Contribution

The novel approach uses transfer learning with physics-encoded neural networks to improve constitutive modeling with sparse experimental data.

## Key findings

- Transfer learning with synthetic and experimental data improves model performance with limited real data.
- Fine-tuning parameters like model architecture and batch size significantly affect simulation accuracy.
- PeNN models outperform synthetic-only models in triaxial test simulations.

## Abstract

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.

The online version contains supplementary material available at 10.1038/s41598-025-34925-0.