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    Multidirectional Gaussian Mixture Models for Nonlinear Uncertainty Propagation

    V. Vittaldev1, R. P. Russell2

    CMES-Computer Modeling in Engineering & Sciences, Vol.111, No.1, pp. 83-117, 2016, DOI:10.3970/cmes.2016.111.083

    Abstract Monte Carlo simulations are an accurate but computationally expensive procedure for approximating the resultant non-Gaussian probability density function (PDF) after propagation of an initial Gaussian PDF through a nonlinear function. Univariate splitting libraries for Gaussian Mixture Models (GMMs) exist with up to five elements in the literature. The number of splits are extended in the present work by generating three homoscedastic univariate splitting libraries with up to 39 elements. Mulitvariate GMMs are typically handled with splits along a single direction. Instead, we generate a regular multidirectional grid over the initial multivariate Gaussian distribution by recursively applying the splitting library along… More >

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