Operator learning in Uncertainty Quantification
In this talk, we discuss operator learning for computing forward surrogates of data-to-solution maps that occur in UQ. It is assumed that the data-to-solution operator is a complex differentiable mapping between two separable Hilbert spaces and that its inputs and outputs are parameterized by stable affine representation systems such as orthonormal bases or frames. Dimension-independent algebraic bounds on the expression rate with respect to the number of network parameters are established. We discuss possible applications such as parametric solutions for second order elliptic PDEs in polygonal domains.