对于结构化电网发电的神经网络
Bari Khairullin1, Sergey Rykovanov2, Rishat Zagidullin2
1Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, bld. 1, Skolkovo, Russia. bari.khairullin@skoltech.ru.
Scientific reports
|April 11, 2025
概括
这项研究引入了一种新的神经网络 (NN) 方法,用于生成适合身体的曲线坐标系统 (BFC). 这种方法简化了复杂几何形状的数值解决方案,通过在正规网格上进行计算.
科学领域:
- 计算数学 计算数学 计算数学
- 数字分析 数字分析
- 几何建模 几何建模
背景情况:
- 部分微分方程 (PDEs) 的数值解在正则域上被简化.
- 复杂的几何通常需要专门的坐标系来进行高效的计算.
- 现有的机身坐标 (BFC) 生成方法可能是繁的,缺乏可区分性.
研究的目的:
- 开发一种基于神经网络 (NN) 的新方法,用于生成2D体型曲线坐标系统 (BFC).
- 为了在正规网格上实现数值解决方案,即使对于复杂的几何形状.
- 为BFCs提供可微分映射,允许准确的雅可比计算.
主要方法:
- 一个前神经网络 (FNN) 被用作几何转换来表示一个diffeomorphism.
- 通过使用类似于物理信息神经网络 (PINN) 解决温斯洛方程的优化系统来训练FNN.
- 该方法侧重于创建BFC,将复杂的物理域映射到正规的计算网格.
主要成果:
- 提出的基于FNN的方法成功地为复杂的几何形状生成2DBFC.
- 生成的映射是可微分的,允许准确计算雅可比矩阵.
- 内部节点分布可以修改而不需要再生整个映射,提供灵活性.
结论:
- 基于NN的方法为生成BFC提供了灵活和高效的替代方案.
- 这种方法通过利用正规网格,简化了复杂领域的PDEs的数值解.
- FNN映射的精确区分和适应性比传统的BFC生成技术具有显著的优势.
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