troegerj/calibration-paper

Reduced and All-at-Once Approaches for Model Calibration and Discovery in Computational Solid Mechanics

This repository provides the research code and data employed for the calibration of constitutive models from full-field displacement data in the following publication:

"Reduced and All-at-Once Approaches for Model Calibration and Discovery in Computational Solid Mechanics"

Citation

@article{roemer_modelCalibration_2024,
    title={Reduced and all-at-once approaches for model calibration and discovery in computational solid mechanics},
    author={Römer, Ulrich and Hartmann, Stefan and Tröger, Jendrik-Alexander and Anton, David and Wessels, Henning and Flaschel, Moritz and De Lorenzis, Laura},
    year={2024},
    journal={arXiv preprint},
    doi={https://doi.org/10.48550/arXiv.2404.16980}
}

Reproducing results

The results in the publication can be reproduced using the provided research codes. Following calibration methods are covered:

• Reduced approaches
  • NLS-FEM (nonlinear least-squares and finite elements)
  • Bayes-FEM (Bayesian inference and finite elements)
  • NLS-PINN (nonlinear least-squares and parametric physics-informed neural networks)
  • Bayes-PINN (Bayesian inference and parametric physics-informed neural networks)
• VFM (virtual fields method)
• All-at-once approaches
  • AAO-PINN (all-at-once using inverse physics-informed neural networks)
  • AAO-FEM (all-at-once using finite elements)
  • AAO-VFM (all-at-once virtual fields method)

Note

Results regarding model discovery can be reproduced with the research code and data provided in this GitHub repository.

The structure of this repository is as follows:

Repository
├── Experimental_Data
├── Reduced
    ├── FEM
    ├── PINN
    ├── NLS
    └── Bayes
└── AAO
    ├── PINN
    └── VFM_FEM

Important

Installation instructions for the specific methods are given in the respective subdirectories.