ArticleNational science review2024
Deciphering and integrating invariants for neural operator learning with various physical mechanisms.
Article in National science review, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 3 papers.
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3 citing papers in PubMed.
- Sliding physical invariant neural operator for long-term prediction of complex dynamics in physical systems.National science review · 2026Article
- Disentangled Representation Learning for Parametric Partial Differential Equations.... International Conference on Learning Representations · 2026Article
- Enhancing neural operator learning with invariants to simultaneously learn various physical mechanisms.National science review · 2024Article
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3 authors.
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Abstract
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 the physical invariant attention neural operator (PIANO) to decipher and integrate the physical invariants 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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