将卷积神经网络应用于带有空间填充曲线的非结构化网格数据
Claire E Heaney1, Yuling Li1, Omar K Matar2
1Applied Modelling and Computation Group, Department of Earth Science and Engineering, Imperial College London, SW7 2AZ, UK.
概括
本研究引入了一种用于非结构化网状数据的新型卷积神经网络 (CNN). 填充空间的曲线将复杂的网状数据转换为1D格式,使CNN直接用于增强的科学计算.
科学领域:
- 计算科学与工程 计算科学与工程
- 人工智能的人工智能
- 数字分析 数字分析
背景情况:
- 卷积神经网络 (CNN) 在结构化网格上表现出色,但在复杂的模拟中常见的非结构化网格数据中扎.
- 在复杂几何或可变分辨率的场景中,非结构化的网格对于解决部分微分方程至关重要.
研究的目的:
- 开发和演示第一个直接适用于非结构化有限元或控制体积网格数据的经典CNN.
- 调整CNN来分析复杂的多维数据,这些数据是从非结构化网格上的模拟中生成的.
主要方法:
- 利用填空曲线 (SFC) 将非结构化的网状节点/细胞映射到1D序列中.
- 将 1D 卷积层应用于 SFC 排序的数据中,使 CNN 处理成为可能.
- 采用了卷积自编码器 (CAE) 架构,具有稀疏层,并探索了多个SFC.
主要成果:
- 成功地将多维非结构化网格数据转换为适合CNN的1D表示.
- 证明了基于SFC的CAE在理想化的问题和现实世界的流体动力学模拟 (流经过一个圆柱体) 上的准确性.
- 展示了SFC方法对更高维度问题的适用性.
结论:
- 提出的基于SFC的CNN方法有效地处理来自非结构化网格的数据,克服了传统CNN的局限性.
- 这种方法为复杂的模拟数据的科学机器学习提供了一个强大的新工具.
- 该技术在涉及非结构化电网的各种科学和工程应用中显示出前景.
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