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Tutorials

Some tutorials to get a first-time user started.

We strongly advise that the user becomes familiar with the MLBLUE, MLMC and MFMC methods before starting, see references below.

Tutorial 1 [.ipynb] [.py]

Currently the one and only. It should walk you through everything needed. For any questions, please contact the developers.

References

  • MLMC:
@article{giles2015multilevel,
  title={Multilevel monte carlo methods},
  author={Giles, Michael B},
  journal={Acta numerica},
  volume={24},
  pages={259--328},
  year={2015},
  publisher={Cambridge University Press}
}
  • MFMC:
@article{peherstorfer2018survey,
  title={Survey of multifidelity methods in uncertainty propagation, inference, and optimization},
  author={Peherstorfer, Benjamin and Willcox, Karen and Gunzburger, Max},
  journal={Siam Review},
  volume={60},
  number={3},
  pages={550--591},
  year={2018},
  publisher={SIAM}
}
  • MLBLUE:
@article{schaden2020multilevel,
  title={On multilevel best linear unbiased estimators},
  author={Schaden, Daniel and Ullmann, Elisabeth},
  journal={SIAM/ASA Journal on Uncertainty Quantification},
  volume={8},
  number={2},
  pages={601--635},
  year={2020},
  publisher={SIAM}
}

@misc{https://doi.org/10.48550/arxiv.2301.07831,
  doi = {10.48550/ARXIV.2301.07831},
  url = {https://arxiv.org/abs/2301.07831},
  author = {Croci, M. and Willcox, K. E. and Wright, S. J.},  
  title = {Multi-output multilevel best linear unbiased estimators via semidefinite programming},
  publisher = {arXiv},
  year = {2023},
 }