On the Control of the 2D Navier–Stokes Equations with Kolmogorov Forcing

Smaoui, Nejib; El-Kadri, Alaa; Zribi, Mohamed

doi:10.1155/2021/3912014

Cited by 1 publication

(1 citation statement)

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“…Experiment E6: Kolmogorov flow with varying viscosity terms ν. We simulate the vorticity fields for 2D NSEs within a periodic domain Ω = [0, 1] × [0, 1] driven by Kolmogorov forcing [ 39 ]:…”

Section: Methodsmentioning

confidence: 99%

Deciphering and integrating invariants for neural operator learning with various physical mechanisms

Zhang,

Meng,

2023

National Science Review

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Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation (PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose Physical Invariant Attention Neural Operator (PIANO) to decipher and integrate the physical invariants (PI) for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional layers. Compared to existing techniques, PIANO can reduce the relative error by 13.6%-82.2% on PDE forecasting tasks across varying coefficients, forces, or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO.

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Section: Methodsmentioning

confidence: 99%