To approximate any (nonlinear) function using orthogonal polynomial, Hermite polynomial is being used for Gaussian weighted function (measure). And the same is true for polynomial chaos approximation. In chaos approximation, the polynomial coefficients are deterministic and there are some approaches like the numerical approximation method (such as Gauss quadrature rule) to approximately evaluate the coefficient value.
My main doubt is that what is the basic difference between orthogonal polynomial and polynomial chaos approximation? How polynomial chaos is different than an orthogonal polynomial approximation?
Any suggestions would be greatly appreciated.