5 papers · 1 filter
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…
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…
DPOT: Auto-Regressive Denoising Operator Transformer for Large-Scale PDE Pre-Training
Zhongkai Hao, Chang Su, Songming Liu +6
Pre-training has been investigated to improve the efficiency and performance of training neural operators in data-scarce settings. However, it is largely in its infancy due to the…
Preconditioning for Physics-Informed Neural Networks
Songming Liu, Chang Su, Jiachen Yao +4
Physics-informed neural networks (PINNs) have shown promise in solving various partial differential equations (PDEs). However, training pathologies have negatively affected the con…
Analyzing the Noise Robustness of Deep Neural Networks
Mengchen Liu, Shixia Liu, Hang Su +2
Deep neural networks (DNNs) are vulnerable to maliciously generated adversarial examples. These examples are intentionally designed by making imperceptible perturbations and often…