物理中故障模式的简单补救措施告知了神经网络
Ghazal Farhani1, Nima Hosseini Dashtbayaz2, Alexander Kazachek3
1National Research Council Canada, Automotive and Surface Transportation, 800 Collip Cir, London, N6G 4X8, Canada.
概括
基于物理学的神经网络 (PINNs) 难以处理复杂的部分微分方程 (PDEs). 使用神经触角内核,这项研究显示了带动量的梯度下降 (GDM) 和Adam优化器可以改善PINN对接,以解决具有挑战性的PDE问题.
科学领域:
- 计算数学 计算数学 计算数学
- 机器学习用于科学
- 数字分析 数字分析
背景情况:
- 基于物理学的神经网络 (PINNs) 对于解决局部微分方程 (PDEs) 有效.
- 对于复杂的PDEs,PINNs面临着趋同的挑战,特别是那些具有大系数或高非线性的人.
- PDE和初始/边界条件损失之间的收率差异阻碍了PINN的表现.
研究的目的:
- 使用神经触角内核 (NTKs) 调查PINNs的训练动态.
- 确定改善PINN对复杂PDEs的收性和准确性的方法.
- 分析优化器对PINNs损失收差异的影响.
主要方法:
- 使用神经触角内核 (NTKs) 进行PINN训练动态的理论分析.
- 研究带动下降梯度 (GDM) 对损失收率的影响.
- 检查亚当优化器在加速融合和减轻差异方面的作用.
主要成果:
- 带动力的梯度下降 (GDM) 显著减少了PDE和初始/边界条件损失之间的收率差距.
- 亚当优化器还加速了收,并减少了差异的影响.
- NTK 分析提供了关于为什么这些优化器可以提高 PINN 性能的理论见解.
结论:
- 用GDM或Adam进行训练的PINN在复杂的PDE中表现出更好的收度和精度.
- 这些发现为提高PINNs在科学计算中的稳定性和适用性提供了一条途径.
- 神经触点内核是理解和改进PDE深度学习模型的宝贵工具.
更多相关视频
10:50Computational Modeling of Retinal Neurons for Visual Prosthesis Research - Fundamental Approaches
Published on: June 21, 2022
1.7K
11:14A Novel Experimental and Analytical Approach to the Multimodal Neural Decoding of Intent During Social Interaction in Freely-behaving Human Infants
Published on: October 4, 2015
10.9K
相关概念视频
01:37Neural Regulation
39.1K
Digestion begins with a cephalic phase that prepares the digestive system to receive food. When our brain processes visual or olfactory information about food, it triggers impulses in the cranial nerves innervating the salivary glands and stomach to prepare for food.
39.1K
01:25Neural Circuits
1.0K
Neural circuits and neuronal pools are two of the main structures found in the nervous system. Neural circuits are networks of neurons that work together to carry out a specific task or process. They consist of interconnected neurons and glial cells, which provide structural and metabolic support.
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
Neuronal pools are collections of nerve cells with similar functions and interact through chemical and electrical signals. These pools include both interneurons (the central neural circuit nodes that...
1.0K
01:26Classification of Systems-I
168
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
168
01:25Multimachine Stability
141
Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:
141