将守恒律融入神经网络，实现稳定且准确的长期物理模拟。
Entropy stable conservative flux form neural networks
- 用熵稳定格式与斜率限制器设计守恒型神经网络
- 在噪声和稀疏数据下仍保持高精度与稳定性
- 适合需要长期预测的物理系统建模任务
我们提出一种熵稳定的守恒通量形式神经网络（CFN），将经典数值守恒律嵌入数据驱动框架，采用熵稳定、二阶、无振荡的Kurganov-Tadmor（KT）格式。所提熵稳定CFN利用斜率限制作为去噪机制，在噪声和稀疏观测环境下，以及光滑与间断区域均能实现精准预测。数值实验表明，该方法在长时间域上同时保持稳定性与守恒性，并成功预测长期模拟中的激波传播速度，且无需训练数据中包含后期状态的先验知识。
原文摘要 · Abstract (English)
We propose an entropy-stable conservative flux form neural network (CFN) that integrates classical numerical conservation laws into a data-driven framework using the entropy-stable, second-order, and non-oscillatory Kurganov-Tadmor (KT) scheme. The proposed entropy-stable CFN uses slope limiting as a denoising mechanism, ensuring accurate predictions in both noisy and sparse observation environments, as well as in both smooth and discontinuous regions. Numerical experiments demonstrate that the entropy-stable CFN achieves both stability and conservation while maintaining accuracy over extended time domains. Furthermore, it successfully predicts shock propagation speeds in long-term simulations, {\it without} oracle knowledge of later-time profiles in the training data.
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。