Researchers have established approximation and learning guarantees for Fourier Neural Operators (FNOs) when applied to time-T solution operators of dissipative evolution equations. The analysis demonstrates that FNOs can efficiently learn these operators if they admit stable spectral discretizations. The study derives FNO approximation bounds and polynomial sample complexity guarantees, with learning rates dependent on factors like the smoothness of the input space, the dimension of the physical domain, and the strength of nonlinear terms and dissipation. AI
IMPACT Establishes theoretical foundations for FNOs in learning complex physical systems, potentially guiding future model development.
RANK_REASON The cluster contains a research paper detailing theoretical advancements in Fourier Neural Operators.
- Allen--Cahn
- alphaXiv
- arXiv
- Cahn--Hilliard Inpainting with the Double Obstacle Potential
- CatalyzeX
- DagsHub
- Fourier Neural Operators
- Gotit.pub
- Hugging Face
- NAVIER STOKES ANALYSIS OF THE AERODYNAMIC PROPERTIES OF COAXIAL ROTORS
- ScienceCast
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