用神经网络求解非线性双曲守恒律的初边值问题，兼顾训练速度与预测精度。
From Initial Data to Boundary Layers: Neural Networks for Nonlinear Hyperbolic Conservation Laws
- 通过求解松弛问题构建神经网络学习框架
- 一维标量案例验证了方法的有效性
- 适合工业级复杂场景的数值模拟
本文研究利用神经网络近似非线性严格双曲守恒律初边值问题的熵解。提出一种通用且系统化的高效可靠学习算法设计框架，兼具训练过程快速收敛与预测结果高精度的特点。该方法基于求解某一相关松弛问题，通过一系列一维标量测试案例进行评估。数值实验表明，所提出的方法具有显著潜力，并可推广至更复杂的工业应用场景。
原文摘要 · Abstract (English)
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and reliable learning algorithms, combining fast convergence during training with accurate predictions. The methodology that relies on solving a certain relaxed related problem is assessed through a series of one-dimensional scalar test cases. These numerical experiments demonstrate the potential of the methodology developed in this paper and its applicability to more complex industrial scenarios.
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