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cs.LG2025
An Imbalanced Learning-based Sampling Method for Physics-informed Neural Networks
Jiaqi Luo, Yahong Yang, Yuan Yuan +2
This paper introduces Residual-based Smote (RSmote), an innovative local adaptive sampling technique tailored to improve the performance of Physics-Informed Neural Networks (PINNs)…
cs.LG2024
Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks
Yahong Yang, Qipin Chen, Wenrui Hao
In this paper, we present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA), aimed at accelerating the training process in contrast to traditional…
cs.LG2024
Newton Informed Neural Operator for Computing Multiple Solutions of Nonlinear Partials Differential Equations
Wenrui Hao, Xinliang Liu, Yahong Yang
Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology,…