36 citations · 51 across the 10 of their papers we have counts for
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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…
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…
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…
NUNO: A General Framework for Learning Parametric PDEs with Non-Uniform Data
Songming Liu, Zhongkai Hao, Chengyang Ying +3
The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly n…
GNOT: A General Neural Operator Transformer for Operator Learning
Zhongkai Hao, Zhengyi Wang, Hang Su +6
Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in prac…
A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs
Songming Liu, Zhongkai Hao, Chengyang Ying +3
We present a unified hard-constraint framework for solving geometrically complex PDEs with neural networks, where the most commonly used Dirichlet, Neumann, and Robin boundary cond…
Bi-level Physics-Informed Neural Networks for PDE Constrained Optimization using Broyden's Hypergradients
Zhongkai Hao, Chengyang Ying, Hang Su +3
Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, exi…