A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation
A long short-term memory neural network-based error estimator for three-dimensional dynamically adaptive mesh generation
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DOI：
10.1063/5.0172020
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发表时间：
2023-10
影响因子：
4.6
通讯作者：
X. Wu;P. Gan;J. Li;F. Fang;X. Zou;C. C. Pain-C.;X. Tang;J. Xin;Z. Wang;J. Zhu
中科院分区：
文献类型：
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作者：
X. Wu;P. Gan;J. Li;F. Fang;X. Zou;C. C. Pain-C.;X. Tang;J. Xin;Z. Wang;J. Zhu
自适应网格在数值建模和仿真中是关键的，它提供了一种有效、精确和灵活地表示复杂物理现象的方法，特别是在处理它们的复杂性和不同的尺度时。然而，从二维（2D）到三维（3D）的过渡带来了巨大的挑战，因为动态自适应网格技术的计算需求呈指数级增长。为了有效解决这一挑战，我们转向人工智能和神经网络的前沿领域。在我们的研究中，我们利用长短期记忆（LSTM）神经网络的创新能力作为误差估计器，用于在2D和3D场景中适应非结构化网格。该LSTM网络基于指定变量预测自适应网格的演化，表现为一种人工智能驱动的体系结构，以优化目标变量的自适应准则。这是通过建立黎曼度规和这些变量之间的直接对应关系来实现的。为了证明我们方法的实际适用性，我们将LSTM误差估计器无缝集成到3D自适应大气模型fluid - atmosphere （fluid - atmos）中，从而在数值模拟期间实现实时网格自适应。我们通过在二维和三维环境下的一系列实验来评估这种方法在模拟精度和计算效率方面的有效性。我们的研究结果不仅揭示了LSTM误差估计器在fluid - atmos中产生的网格模式与传统误差估计器产生的网格模式非常相似，而且强调了其在提高模拟精度方面的优越性能。值得注意的是，随着节点数量的增加，与fluid - atmos中的传统网格生成器相比，LSTM网格生成器在3D情况下大大减少了CPU时间需求，最多可减少50%，突出了其卓越的计算效率。
Adaptive meshes are pivotal in numerical modeling and simulation, offering a means to efficiently, precisely, and flexibly represent intricate physical phenomena, particularly when grappling with their intricacies and varying scales. However, the transition from two dimensions (2D) to three dimensions (3D) poses a substantial challenge, as the computational demands of dynamically adaptive mesh techniques increase exponentially. Addressing this challenge effectively, we turn to the cutting-edge realm of artificial intelligence and neural networks. In our study, we harness the innovative power of a long short-term memory (LSTM) neural network as an error estimator for adapting unstructured meshes in both 2D and 3D scenarios. This LSTM network predicts the evolution of the adaptive grid based on specified variables, presenting itself as an artificial intelligence-driven architecture to optimize the adaptive criterion for the target variable. This is achieved by establishing a direct correspondence between the Riemann metric and these variables. To demonstrate the practical applicability of our approach, we seamlessly integrate the LSTM error estimator into the 3D adaptive atmospheric model Fluidity-Atmosphere (Fluidity-Atmos), thereby enabling real-time mesh adaptation during numerical simulations. We assess the effectiveness of this method in terms of simulation precision and computational efficiency through a series of experiments in both 2D and 3D settings. Our results not only reveal that the mesh patterns generated by the LSTM error estimator within Fluidity-Atmos closely resemble those produced by traditional error estimators but also underscore its superior performance in enhancing simulation accuracy. Notably, as the number of nodes increases, the LSTM mesh generator substantially reduces CPU time requirements by up to 50% in 3D cases compared to the conventional mesh generator within Fluidity-Atmos, highlighting its remarkable computational efficiency.