Resource on Polynomial Chaos Expansion

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Hi Community Members,

Please could anyone recommend a good and simplified book/ paper(s) / other resource where I could read about ‘Polynomial Chaos Expansion’ with basic information of the process . I wish to complement this with the uqlab manual on this subject. Just a foundational text on this concept simply presented. Thoughts appreciated by you all.

Thanks

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Dear Aghatise

You can find a more detailed presentation on polynomial chaos expansions in this monograph (Chapter 4), or in this dedicated book chapter.

Other important references includes:

  1. Xiu, D., Karniadakis, G. E., 2002. The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations, SIAM Journal on Scientific Computing, 24, 619–644.
  2. Soize, C., Ghanem, R., 2004. Physical systems with random uncertainties: chaos representations with arbitrary probability measure. SIAM Journal on Scientific Computing, 26, 395–410.
  3. Xiu, D., 2010. Numerical methods for stochastic computations – A spectral method approach. Princeton University press.

Best regards
Bruno

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Thank you so much Prof for the reference. Truly appreciated.