Neural Operators
Fourier, DeepONet, and graph neural operators for PDE solution maps.
Neural Operators. Fourier, DeepONet, and graph neural operators for PDE solution maps.
Recent technical contributions
A handful of recent papers carry the methodological frontier of neural operators forward. Fourier Neural Operator for Parametric Partial Differential Equations (Li et al., 2021) is a primary reference for this area and develops new techniques or results that downstream work builds on. Neural Operator: Learning Maps Between Function Spaces (Kovachki et al., 2023) pushes the technical state of the art and is widely cited in subsequent work on the topic.
Open methodological questions for neural operators include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- paper · primary · 2021li-zongyi-2021, kovachki-2021, azizzadenesheli-2021, liu-burigede-2021, bhattacharya-2021, stuart-2021, anandkumar-2021
- paper · primary · 2023kovachki-2023, li-zongyi-2023, liu-burigede-2023, azizzadenesheli-2023, bhattacharya-2023, stuart-2023, anandkumar-2023
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