Learning in latent spaces improves the predictive accuracy of deep neural operators

Understand

Operator regression provides a powerful means of constructing discretization-invariant emulators for partial-differential equations (PDEs) describing physical systems.

• Neural operators specifically employ deep neural networks to approximate mappings between infinite-dimensional Banach spaces.
• As data-driven models, neural operators require the generation of labeled observations, which in cases of complex high-fidelity models result in high-dimensional datasets containing redundant and noisy features, which can hinder gradient-based optimization.
• Mapping these high-dimensional datasets to a low-dimensional latent space of salient features can make it easier to work with the data and also enhance learning.