5 papers
SSBE-PINN: A Sobolev Boundary Scheme Boosting Stability and Accuracy in Elliptic/Parabolic PDE Learning
Qixuan Zhou, Chuqi Chen, Tao Luo +1
Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs), yet they often fail to achieve accurate convergence…
Quantifying Training Difficulty and Accelerating Convergence in Neural Network-Based PDE Solvers
Chuqi Chen, Qixuan Zhou, Yahong Yang +2
Neural network-based methods have emerged as powerful tools for solving partial differential equations (PDEs) in scientific and engineering applications, particularly when handling…
Demystifying Lazy Training of Neural Networks from a Macroscopic Viewpoint
Yuqing Li, Tao Luo, Qixuan Zhou
In this paper, we advance the understanding of neural network training dynamics by examining the intricate interplay of various factors introduced by weight parameters in the initi…
A priori Estimates for Deep Residual Network in Continuous-time Reinforcement Learning
Shuyu Yin, Qixuan Zhou, Fei Wen +1
Deep reinforcement learning excels in numerous large-scale practical applications. However, existing performance analyses ignores the unique characteristics of continuous-time cont…
On Residual Minimization for PDEs: Failure of PINN, Modified Equation, and Implicit Bias
Tao Luo, Qixuan Zhou
As a popular and easy-to-implement machine learning method for solving differential equations, the physics-informed neural network (PINN) sometimes may fail and find poor solutions…