Neural integration for constitutive equations – HANDS-ON for experimental data

This repository contains Jupyter notebooks and code developed for the 2025 ALERT Olek Zienkiewicz Doctoral School on Constitutive modelling of geomaterials - Session: Constitutive modelling meets Machine Learning.

📌 More details: ALERT OZ School 2025 Program

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📂 Hands-on Exercises

Two exercises are considered, both uses experimental results of a sand specimen subjected to drained triaxial compression from SoilModels. The first exercise considers a filtered (smoothed) version of the original dataset, the second uses the original, raw dataset. The filtered data is used to enable a fast training which can be effectively used to vary the structure of the network (and its hyper-parameters).

I. Learning constitutive equations from experiments – [sand] training & validation

• Material: Sand with scattered gravel (origin: Dobrany, Czech Republic)
• Tests: Drained triaxial compression
• Dataset: Smoothed version of the experimental data

II. Learning constitutive equations from experiments – [sand-raw] training & validation

• Material: Sand with scattered gravel (origin: Dobrany, Czech Republic)
• Tests: Drained triaxial compression
• Dataset: Original experimental data

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📖 References

If you find this repository helpful, please consider citing:

Masi, F., & Einav, I. (2023). Neural integration for constitutive equations using small data. Computer Methods in Applied Mechanics and Engineering, 420, 116698.

@article{masi2024neural,
  title={Neural integration for constitutive equations using small data},
  author={Masi, Filippo and Einav, Itai},
  journal={Computer Methods in Applied Mechanics and Engineering},
  volume={420},
  pages={116698},
  year={2024},
  publisher={Elsevier}
}

@article{HandsOnNICE,
  title={NICE - Experiments Hands-on},
  author={Masi, Filippo and Louvard, Enzo},
  year={2025},
  url={https://github.com/filippo-masi/ALERT-OlekZienkiewicz-ML}
}

Authors: Filippo Masi, Enzo Louvard