On the influence of over-parameterization in manifold based surrogates and deep neural operators. (arXiv:2203.05071v1 [cs.LG])

Constructing accurate and generalizable approximators for complex
physico-chemical processes exhibiting highly non-smooth dynamics is
challenging. In this work, we propose new developments and perform comparisons
for two promising approaches: manifold-based polynomial chaos expansion (m-PCE)
and the deep neural operator (DeepONet), and we examine the effect of
over-parameterization on generalization. We demonstrate the performance of
these methods in terms of generalization accuracy by solving the 2D
time-dependent Brusselator reaction-diffusion system with uncertainty sources,
modeling an autocatalytic chemical reaction between two species. …

arxiv influence manifold operators