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| 数据驱动的高分辨率CCWENO-ANN算法 |
| Data-Driven High-Resolution CCWENO-ANN Algorithm |
| 投稿时间：2025-01-17 修订日期：2025-02-26 |
| DOI： |
| 中文关键词: 双曲守恒律 数据驱动 CCWENO 重构 神经网络 机器学习 |
| 英文关键词:Hyperbolic conservation law Data-driven CCWENO reconstruction Neural network Machine learning |
| 基金项目:国家自然科学基金项目（面上项目，重点项目，重大项目） |
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| 中文摘要: |
| 为准确求解双曲守恒律，得到高分辨率数值结果，本文将数据驱动与三阶CCWENO(Compact Central Weighted Essentially Non-Oscillatory)格式相结合，提出了一种基于数据驱动的CCWENO-ANN高分辨率格式求解双曲守恒律。通过构建人工神经网络的归一化校准层和稀疏化层，引入适当的先验知识，加快收敛速度；同时，损失函数动态地调整神经网络输出与理想权重之间的偏差，并在合适的数据集上采用监督学习策略进行离线训练，以提高神经网络性能。通过一维无粘Burgers方程，一维Euler方程，二维无粘Burgers方程以及二维Euler方程验证算法性能，结果表明本文提出的CCWENO-ANN继承了传统CCWENO格式的收敛性，能够准确捕捉激波和接触间断，具有鲁棒性强、低耗散和高分辨率的优点。 |
| 英文摘要: |
| To accurately solve hyperbolic conservation laws and obtain high-resolution numerical results, this paper combined data-driven with third-order CCWENO(Compact Central Weighted Essentially Non-Oscillatory) scheme, and proposed a data-driven CCWENO-ANN high-resolution scheme for hyperbolic conservation laws. By constructing the normalized calibration layer and sparse layer of artificial neural network, the appropriate prior knowledge is introduced to accelerate the convergence speed. At the same time, the loss function dynamically adjusts the deviation between the outputs of the neural network and the ideal weights, and uses the supervised learning strategy to train the neural network offline on the appropriate data set to improve the performance of the neural network. By solving one-dimensional inviscid Burgers equations, one-dimensional Euler equations, two-dimensional inviscid Burgers equations and two-dimensional Euler equations, we aim to evaluate the performance of the algorithm. The results show that the proposed CCWENO-ANN inherits the convergence of the traditional CCWENO scheme and can accurately capture shock waves and contact discontinuities, and has the advantages of robustness, low dissipation and high resolution. |
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