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

作　　者：Rui Zhang Qi Meng Zhi-Ming Ma 

机构地区：[1]Academy of Mathematics and Systems Science,Chinese Academy of Sciences(CAS),Beijing 100190,China [2]Microsoft Research,Beijing 100080,China

出　　处：《National Science Review》2024年第4期105-116,共12页国家科学评论（英文版）

基　　金：This work was supported by the National Key R&D Program of China(2020YFA0712700).

摘　　要：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.

关 键 词：neural operator PDE solver contrastive learning physical invariants 

分 类 号：O241.82[理学—计算数学] TP18[理学—数学]