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cs.LG2025
Accelerating PDE-Constrained Optimization by the Derivative of Neural Operators
Ze Cheng, Zhuoyu Li, Xiaoqiang Wang +4
PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to tradition…
cs.LG2025
Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solving
Jianing Huang, Kaixuan Zhang, Youjia Wu +1
Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between f…
cs.LG2024★ 1 cited
Reference Neural Operators: Learning the Smooth Dependence of Solutions of PDEs on Geometric Deformations
Ze Cheng, Zhongkai Hao, Xiaoqiang Wang +6
For partial differential equations on domains of arbitrary shapes, existing works of neural operators attempt to learn a mapping from geometries to solutions. It often requires a l…