一种新的局部时间脱方Wasserstein-2方法用于训练随机神经网络以重建动态系统中的不确定参数
Mingtao Xia1, Qijing Shen2, Philip K Maini3
1Department of Mathematics, University of Houston, Philip Guthrie Hoffman Hall, 3551 Cullen Blvd, Houston, TX, 77204, USA.
概括
这项研究引入了一种使用时间数据来估计动态系统中的不确定参数的新方法. 该技术有效地重建参数分布,提高模型的准确性.
科学领域:
- 计算数学
- 动态系统理论
- 机器学习
背景情况:
- 动态系统通常涉及难以估计的不确定的参数.
- 重建这些参数分布对于准确的系统建模和预测至关重要.
- 现有的方法可能难以处理参数空间的复杂性和维度.
研究的目的:
- 提出和分析一种用于重建动态系统中的参数分布的新方法.
- 用特定的损失函数进行训练的随机神经网络的有效性.
- 在各种动态系统中验证方法的性能.
主要方法:
- 开发一个局部时间脱方Wasserstein-2方法.
- 应用一个随机神经网络模型.
- 通过尽量减少损失功能来训练神经网络.
- 使用不同动态系统的数值示例进行验证.
主要成果:
- 拟议的局部时间脱方Wasserstein-2方法有效地重建参数分布.
- 用这种损失函数训练的随机神经网络提供了准确的近似值.
- 这种方法在各种动态系统中显示出强大的性能.
结论:
- 开发的方法为动态系统中的参数估计提供了强大的工具.
- 这种方法增强了对具有固有不确定性的系统的理解和建模.
- 这些发现对依赖动态系统建模的领域有影响.
相关概念视频
01:21Linear Approximation in Time Domain
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Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
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01:23Linear time-invariant Systems
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01:18Second Order systems II
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01:27State Space Representation
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01:24BIBO stability of continuous and discrete -time systems
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