English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Neural operators have been explored as surrogate models for simulatingphysical systems to overcome the limitations of traditional partialdifferential equation (PDE) solvers. However, most existing operator learningmethods assume that the data originate from a single physical mechanism,limiting their applicability and performance in more realistic scenarios. Tothis end, we propose Physical Invariant Attention Neural Operator (PIANO) todecipher and integrate the physical invariants (PI) for operator learning fromthe PDE series with various physical mechanisms. PIANO employs self-supervisedlearning to extract physical knowledge and attention mechanisms to integratethem into dynamic convolutional layers. Compared to existing techniques, PIANOcan reduce the relative error by 13.6\%-82.2\% on PDE forecasting tasks acrossvarying coefficients, forces, or boundary conditions. Additionally, varieddownstream tasks reveal that the PI embeddings deciphered by PIANO align wellwith the underlying invariants in the PDE systems, verifying the physicalsignificance of PIANO. The source code will be publicly available at:https://github.com/optray/PIANO.

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