BaPC Matlab Toolbox: Bayesian Arbitrary Polynomial Chaos
Updated 23 Mar 2020
BaPC Matlab Toolbox offers an advanced framework for stochastic model calibration and parameter inference based on the arbitrary polynomial chaos expansion (aPC) and strict Bayesian principles. BaPC framework follows the idea of aPC technique (Oladyshkin and Nowak, 2012) and can use arbitrary distributions for modelling parameters, which can be either discrete, continuous, or discretized continuous and can be specified either analytically, numerically as histogram or as raw data sets. BaPC Matlab Toolbox approximates the dependence of simulation model output on model parameters by expansion in an orthogonal polynomial basis and the resulting response surface can be seen as a reduced (surrogate) model. BaPC Matlab Toolbox employs an iterative Bayesian approach (Oladyshkin and Nowak, 2013) in incorporate the available measurement data and to construct the accurate reduced model in the relevant regions of high posterior probability.
Stuttgart Center for Simulation Science,
Department of Stochastic Simulation and Safety Research for Hydrosystems,
Institute for Modelling Hydraulic and Environmental Systems,
University of Stuttgart, Pfaffenwaldring 5a, 70569 Stuttgart
Sergey Oladyshkin (2023). BaPC Matlab Toolbox: Bayesian Arbitrary Polynomial Chaos (https://www.mathworks.com/matlabcentral/fileexchange/74006-bapc-matlab-toolbox-bayesian-arbitrary-polynomial-chaos), MATLAB Central File Exchange. Retrieved .
Oladyshkin, S., and W. Nowak. “Data-Driven Uncertainty Quantification Using the Arbitrary Polynomial Chaos Expansion.” Reliability Engineering & System Safety, vol. 106, Elsevier BV, Oct. 2012, pp. 179–90, doi:10.1016/j.ress.2012.05.002.
Oladyshkin, Sergey, and Wolfgang Nowak. “Incomplete Statistical Information Limits the Utility of High-Order Polynomial Chaos Expansions.” Reliability Engineering & System Safety, vol. 169, Elsevier BV, Jan. 2018, pp. 137–48, doi:10.1016/j.ress.2017.08.010.
Oladyshkin S., Class H. and Nowak W. Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations. Computational Geosciences, 17(4), 671-687, 2013. doi: 10.1007/s10596-013-9350-6.
Oladyshkin S., Schroeder P., Class H. and Nowak W. Chaos expansion based Bootstrap filter to calibrate CO2 injection models. Energy Procedia, 40, 398-407, 2013. doi: 10.1016/j.egypro.2013.08.046.
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