研究物理信息损失下神经网络的谱偏差，揭示NTK结构与收敛特性。
Neural Tangent Kernel of Neural Networks with Loss Informed by Differential Operators
- 基于微分算子构建物理约束损失，扩展NTK理论框架
- 发现微分算子不显著加快特征值衰减速率
- 适用于需要理解物理引导网络收敛机制的研究者
谱偏差是神经网络训练中的重要现象，可用神经正切核（NTK）理论解释。本文发展了含物理信息损失的深度神经网络的NTK理论，揭示了初始化与训练过程中NTK的收敛性及其显式结构。研究发现，在大多数情况下，损失函数中的微分算子并不会导致更快的特征值衰减速率或更强的谱偏差。实验结果验证了该理论的合理性。
原文摘要 · Abstract (English)
Spectral bias is a significant phenomenon in neural network training and can be explained by neural tangent kernel (NTK) theory. In this work, we develop the NTK theory for deep neural networks with physics-informed loss, providing insights into the convergence of NTK during initialization and training, and revealing its explicit structure. We find that, in most cases, the differential operators in the loss function do not induce a faster eigenvalue decay rate and stronger spectral bias. Some experimental results are also presented to verify the theory.
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