One of the main issue in engineering is the disconnect between experimentalists and people running codes all day long. The disconnect occurs at several levels but one that is the most painful is the inability to iterate fast enough between the results of some code and the results of some experiments. Part of the problem stems from the experiments sometimes costing millions of dollars, another issue is that there is little infrastructure built-in forward codes to estimate uncertainties based on uncertainties of the model. Some of this hardly being addressed in the engineering curriculum and this is why I would have to salute the effort made at Duke to remedy this though the SAMSI effort program on Uncertainty Quantification. It turns out there is a connection to Compressive Sensing as shown in the different presentations by Alireza Doostan ( we featured him before)
- Stochastic PDEs, Sparse Approximations, and Compressive Sampling
- A Compressive Sampling Approach to Sparse Polynomial Chaos Expansions
So the bounds on Legendre Polynomials and Spherical Harmonics are not so abstract after all!
If you wonder what Polynomial chaos coefficients are, you may want to look into these tutorials and other presentations:
- Mini-tutorial On Uncertainty Quantiﬁcation: Intrusive UQ Propagation Methods by Alireza Doostan
- Sensitivity analysis and polynomial chaos for differential equations by Dongbin Xiu ( The videos for this talk are here)
- Nonintrusive Polynomial Chaos and Stochastic Collocation Methods for Uncertainty Analysis and Design by Michael S. Eldred.
- Inverse Problem and Calibration tutorial lecture by Peter Kitanidis .
More information about the SAMSI program on Uncertainty Quantification:
- High Dimensional Approximation for Uncertainty Quantification - November 10, 2011
- SAMSI/Sandia Summer School on Uncertainty Quantification - June 20-24, 2011
I have duplicated some elements of this entry and more on the Robust Mathematical Modeling blog.
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