7 papers
A Geometry-Aware Operator Learning Framework for Interface Problems on Varying Domains
Shanshan Xiao, Ye Li, Zhongyi Huang +1
Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for trad…
Image Segmentation via Variational Model Based Tailored UNet: A Deep Variational Framework
Kaili Qi, Wenli Yang, Ye Li +1
Traditional image segmentation methods, such as variational models based on partial differential equations (PDEs), offer strong mathematical interpretability and precise boundary m…
Noise-robust Contrastive Learning for Critical Transition Detection in Dynamical Systems
Wenqi Fang, Ye Li
Detecting critical transitions in complex, noisy time-series data is a fundamental challenge across science and engineering. Such transitions may be anticipated by the emergence of…
A Fast Initialization Method for Neural Network Controllers: A Case Study of Image-based Visual Servoing Control for the multicopter Interception
Chenxu Ke, Congling Tian, Kaichen Xu +2
Reinforcement learning-based controller design methods often require substantial data in the initial training phase. Moreover, the training process tends to exhibit strong randomne…
Convergence of Implicit Gradient Descent for Training Two-Layer Physics-Informed Neural Networks
Xianliang Xu, Ting Du, Wang Kong +3
The optimization algorithms are crucial in training physics-informed neural networks (PINNs), as unsuitable methods may lead to poor solutions. Compared to the common gradient desc…
Convergence Analysis of Natural Gradient Descent for Over-parameterized Physics-Informed Neural Networks
Xianliang Xu, Ting Du, Wang Kong +3
In the context of over-parameterization, there is a line of work demonstrating that randomly initialized (stochastic) gradient descent (GD) converges to a globally optimal solution…