评估物理信息的神经网络中的单个乘法神经元模型,用于微分方程.
1Department of Statistics, Giresun University, Giresun, 28200, Turkey. melih_agraz@brown.edu.
Scientific reports
|August 17, 2024
概括
一个新的模仿单个乘法神经元模型 (模仿-SMNM) 与传统的物理信息神经网络 (PINNs) 相比,为微分方程提供了更快,更有效的解决方案. 模仿-SMNM实现了计算速度的五倍增长.
科学领域:
- 计算数学 计算数学 计算数学
- 人工智能的人工智能
- 神经网络架构 神经网络架构
背景情况:
- 人工神经网络 (ANN) 是用于估计和分类的强大工具.
- 基于物理学的神经网络 (PINNs) 通过将边界条件集成到损失函数中,有效地解决微分方程.
- 确定最佳的ANN架构 (神经元,层) 仍然是一个挑战.
研究的目的:
- 在PINNs框架内研究单个增殖神经元模型 (SMNM) 的应用.
- 在PINNs中解决与传统SMNM遇到的融合问题.
- 引入和评估一个改进的"模仿单个倍增神经元模型" (模仿-SMNM),以提高计算效率和融合.
主要方法:
- 在特定微分方程的PINNs框架内实施SMNM.
- 开发模拟-SMNM架构,以保持概念优势,同时确保融合.
- 对真实PINNs,传统SMNM和模仿SMNM进行比较分析.
主要成果:
- 传统的SMNM在应用于微分方程时未能收.
- 真正的PINN成功地解决了方程.
- 模仿SMNM展示了建筑简单性,计算可行性和融合.
- 在3万个时代后,模仿SMNM实现了与真实PINN相比计算速度的五倍增长.
结论:
- 由于融合问题,传统的SMNM不适合PINNs框架.
- 拟议的模拟-SMNM为在PINNs上下文中解决微分方程提供了一个高效和计算可行的替代方案.
- 在特定应用中,模仿SMNM在标准PINN上提供了显著的速度优势.
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