神经普通微分方程用于学习和超分系统动态跨分叉
Eva van Tegelen1,2, George van Voorn1, Ioannis N Athanasiadis2
1Biometris, Wageningen University and Research, Wageningen, The Netherlands.
Chaos (Woodbury, N.Y.)
|October 22, 2025
概括
神经常规微分方程使用时间序列数据预测系统的分叉. 这种机器学习方法预测了超越训练数据的关键过渡,推进了动态系统分析.
科学领域:
- 动态系统和机器学习
- 计算物理 计算物理
- 非线性动力学是一种非线性动力学.
背景情况:
- 预测动态系统中的关键过渡和分叉结构对于理解系统转移至关重要.
- 现有的分析分叉的机器学习方法通常仅限于离散时间模型和局部现象.
- 神经常规微分方程 (NODE) 是一种数据驱动的方法,可以从时间序列数据中学习系统动态.
研究的目的:
- 开发和演示使用NODE的机器学习框架,用于从时间序列数据中学习和预测分叉.
- 克服目前机器学习方法中离散时间方法和局部分叉分析的局限性.
- 调查NODE在预测超出训练数据参数范围的分叉的能力.
主要方法:
- 利用神经常规微分方程 (NODE) 作为数据驱动的框架来学习系统动力学.
- 在时间序列数据上训练NODE学习参数依赖向量场,从而揭示底层的分叉结构.
- 将NODE方法应用于各种测试案例,包括洛伦茨系统,罗斯勒系统和捕食者-猎物模型.
主要成果:
- 证明NODE可以直接从时间序列数据中准确地恢复分叉结构.
- 展示了NODE能够有效地预测分叉的能力,即使是不包括在培训数据集中的参数区域.
- 他成功地将该方法应用于模拟从非混乱到混乱行为的过渡 (Lorenz),混沌到周期翻倍 (Rössler) 和导致崩 (掠食者-猎物) 的全球分叉.
结论:
- 神经常规微分方程为学习系统动态和从时间序列数据预测分叉提供了强大的工具.
- NODE框架扩展了机器学习能力,用于分析动态系统中的关键转换,包括超越训练数据参数.
- 这种方法为预测突然转变和理解各种科学领域的复杂行为提供了一个有希望的途径.
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