Approximation and Uncertainty Quantification of Stochastic Systems with Arbitrary Input Distributions using Weighted Leja Interpolation
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Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of a stochastic system's input parameters are not normal, uniform, or closely related ones, due to the lack of suitable interpolation nodes. This paper suggests the use of weighted Leja node sequences as a remedy to this situation. We present the recently introduced weighted Leja interpolation rules, along with a dimension-adaptive sparse interpolation algorithm, to be employed in the case of high-dimensional input uncertainty. The performance and reliability of the suggested approach is verified by the results of three numerical experiments, where the respective models feature extreme value and truncated normal input distributions. The suggested approach is also compared against a well-established polynomial chaos method and found to be either comparable or superior in terms of approximation and statistical moment estimation accuracy.
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