Neural and spectral operator surrogates for Gaussian random field inputs
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In this talk we discuss the use of neural network or polynomial based operator surrogates to approximate smooth maps between infinite-dimensional Hilbert spaces. Such surrogates have a wide range of applications in uncertainty quantification and parameter estimation problems. The error is measured in the $L^2$-sense with respect to a Gaussian measure on the input space. Under suitable assumptions, we show that algebraic and dimension-independent convergence rates can be achieved. For the polynomial based variant we provide a constructive interpolation algorithm.
