自适应采样让物理神经网络更准捕捉相变界面。
Auto-Adaptive PINNs with Applications to Phase Transitions
- 根据网络梯度设计动态采样策略，聚焦关键区域。
- 在阿伦-卡恩方程上实现无后处理的界面精确解析。
- 适合需高精度模拟相变过程的研究者。
我们提出一种针对物理信息神经网络（PINNs）训练的自适应采样方法，支持基于任意问题相关启发式规则的采样，该规则可依赖网络及其梯度。特别地，我们聚焦于阿伦-卡恩方程，旨在不进行后处理重采样的情况下，准确解析特征界面区域。实验表明，该方法在性能上优于基于残差的自适应框架。
原文摘要 · Abstract (English)
We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs) which allows for sampling based on an arbitrary problem-specific heuristic which may depend on the network and its gradients. In particular we focus our analysis on the Allen-Cahn equations, attempting to accurately resolve the characteristic interfacial regions using a PINN without any post-hoc resampling. In experiments, we show the effectiveness of these methods over residual-adaptive frameworks.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。