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This chapter provides a mathematical introduction to operator surrogates, which are finite-parametric maps approximating complex (typically nonlinear) operators between infinite-dimensional spaces, and presents convergence rate bounds for holomorphic operators that depend on the number of trainable parameters and the r...
We prove expression rate bounds of finite-parametric, spectral and neural surrogates for holomorphic maps between separable Hilbert spaces. The surrogates have an encoder-approximator-decoder architecture, with Karhunen-Lo\'{e}ve encoders and frame decoders. We prove expression rate bounds for two classes of finite-par...
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