| Abstract: |
| In this talk, we will discuss collocation method via compressive sampling for recovering arbitrary Polynomial Chaos expansions (aPC). Our approach is motivated by the desire to use aPC to quantify uncertainty in models with random parameters. The aPC uses the statistical moments of the input random variables to establish the polynomial chaos expansion and can cope with arbitrary distributions with arbitrary probability measures. To identify the aPC expansion coefficients, we use the idea of Christoffel sparse approximation. We present theoretical analysis to motivate the algorithm. Numerical examples are also provided to show the efficiency of our method. |
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