On the influence of over-parameterization in manifold based surrogates and deep neural operators

Understand

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.
• We first propose an extension of the m-PCE by constructing a mapping between latent spaces formed by two separate embeddings of input functions and output QoIs.