What is it about?
The proposed Banach neural operator (BNO) explicitly incorporates Koopman spectral theory and DMD into a trainable deep operator learning pipeline. BNO evolves dynamics in a Koopman modal space spanned by approximate eigenfunctions, enabling interpretable sequence-to-sequence (seq2seq) forecasting, zero-shot super-resolution, and robust generalization across spatial scales.
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Photo by MARIOLA GROBELSKA on Unsplash
Why is it important?
BNO achieves robust zero-shot super-resolution in unsteady flow prediction and consistently outperforms conventional Koopman-based methods and deep learning models.
Perspectives
Bridges classical fluid dynamics (Navier–Stokes) with modern machine learning (neural operators, Koopman theory, DMD).
Bo Zhang
Northern Illinois University
Read the Original
This page is a summary of: Banach neural operator for Navier–Stokes equations, Physics of Fluids, August 2025, American Institute of Physics,
DOI: 10.1063/5.0284818.
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