Welcome to UncertainSCI’s documentation!


UncertainSCI source code

About UncertainSCI

UncertainSCI is a Python-based toolkit that harnesses modern techniques to estimate model and parametric uncertainty, with a particular emphasis on needs for biomedical simulations and applications. This toolkit enables non-intrusive integration of these techniques with well-established biomedical simulation software.

Currently implemented in UncertainSCI is Polynomial Chaos Expansion (PCE) with a number of input distributions. For more information about these techniques, see: [BNO20, CM17, GNYZ18, Nar18]


Jake Bergquist, Dana Brooks, Zexin Liu, Rob MacLeod, Akil Narayan, Sumientra Rampersad, Lindsay Rupp, Jess Tate, Dan White


This project was supported by grants from the National Institute of Biomedical Imaging and Bioengineering (U24EB029012) from the National Institutes of Health.



Kyle M. Burk, Akil Narayan, and Joseph A. Orr. Efficient sampling for polynomial chaos-based uncertainty quantification and sensitivity analysis using weighted approximate fekete points. International Journal for Numerical Methods in Biomedical Engineering, 36(11):e3395, 2020. URL: https://onlinelibrary.wiley.com/doi/abs/10.1002/cnm.3395, doi:https://doi.org/10.1002/cnm.3395.


Albert Cohen and Giovanni Migliorati. Optimal weighted least-squares methods. SMAI Journal of Computational Mathematics, 3:181–203, 2017. arxiv:1608.00512 [math.NA]. doi:10.5802/smai-jcm.24.


L. Guo, A. Narayan, L. Yan, and T. Zhou. Weighted Approximate Fekete Points: Sampling for Least-Squares Polynomial Approximation. SIAM Journal on Scientific Computing, 40(1):A366–A387, 2018. arXiv:1708.01296 [math.NA]. URL: http://epubs.siam.org/doi/abs/10.1137/17M1140960, doi:10.1137/17M1140960.


S.K. Gupta and W.V. Harper. Sensitivity/Uncertainty Analysis of a Borehole Scenario Comparing Latin Hypercube Sampling and Deterministic Sensitivity Approaches. Technical Report BMI/ONWI-516, Battelle Memorial Institute, Office of Nuclear Waste Isolation, 1983.


Akil Narayan. Computation of induced orthogonal polynomial distributions. Electronic Transactions on Numerical Analysis, 50:71–97, 2018. arXiv:1704.08465 [math]. URL: https://epub.oeaw.ac.at?arp=0x003a184e, doi:10.1553/etna_vol50s71.

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