带有不规则和杂数据的神经普通微分方程
1Max Planck Institute for Dynamics of Complex Technical Systems, Standtorstrasse 1, 39106 Magdeburg, Germany.
Royal Society open science
|July 21, 2023
概括
这项研究引入了一种使用深度神经网络和神经普通微分方程 (ODEs) 来基于噪音数据建模物理过程的新方法. 该方法有效地重建微分方程,即使采用不规则的抽样和噪声.
科学领域:
- 计算科学 计算科学
- 应用数学 应用数学 应用数学
- 机器学习 机器学习
背景情况:
- 测量噪声和不规则的采样是收集物理过程数据的常见挑战.
- 准确的动态建模对于解释数据和理解物理系统至关重要.
- 现有的方法可能会与杂或不规则采样的时间序列数据作斗争.
研究的目的:
- 从杂,不规则的采样数据中开发一种强大的学习微分方程的方法.
- 将深度神经网络与神经普通微分方程 (ODEs) 集成,以进行增强的建模.
- 为了解决标准神经ODE方法在处理测量噪音方面的局限性.
主要方法:
- 一个新的框架结合了两个神经网络:一个用于隐式数据表示,另一个用于矢量场建模.
- 这些网络的集成使用神经常规微分方程 (ODEs) 作为约束.
- 使用各种微分方程的数据进行演示,包括与标准神经ODEs进行比较.
主要成果:
- 拟议的框架有效地从噪音测量中学习动态模型.
- 该方法成功处理不规则采样数据,其中依赖变量在同一时间点无法使用.
- 具体结构的整合,如二级动态,被证明是可行的.
结论:
- 集成的深度神经网络和神经ODE方法提供了一个强大的工具,用于模拟物理过程与噪音数据.
- 这种方法在处理现实世界,不完美的测量时,比标准的神经ODEs提供了显著的优势.
- 组合技术可以进一步提高拟议的建模方法的性能和可靠性.
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