Showing math.NAShow all
3 papers · 1 filter
math.NA2026
Deep neural network yields regularization for ill-posed inverse problems
Qiao Zhu, Lan Wang, Ye Zhang
This paper studies the regularization of ill-posed inverse problems by deep neural networks (DNNs). We extend architecture-based regularization from shallow networks to deep models…
math.NA2025
Shallow neural network yields regularization for ill-posed inverse problems
Lan Wang, Qiao Zhu, Bangti Jin +1
In this paper, we develop regularization theory for neural network approximations of general ill-posed operator equations with noisy data. Within the framework of iterative regular…
math.NA2025
Deep asymptotic expansion method for solving singularly perturbed time-dependent reaction-advection-diffusion equations
Qiao Zhu, Dmitrii Chaikovskii, Bangti Jin +1
Physics-informed neural network (PINN) has shown great potential in solving partial differential equations. However, it faces challenges when dealing with problems involving steep…