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EgPDE-Net:构建连续神经网络,以对外变量进行时间序列预测

Penglei Gao, Xi Yang, Rui Zhang

IEEE transactions on cybernetics

|February 28, 2024

概括

本研究引入了一种新的连续时间模型,用于多变量时间序列分析,通过结合外源变量来学习部分微分方程 (PDEs). 该模型显著提高了预测准确性,超过了现有方法.

科学领域:

时间序列分析时间序列分析
动态系统建模动态系统建模
机器学习用于科学计算

背景情况:

外源变量显著影响时间序列预测,但它们的序列间相关性和时间依赖性在当前的连续时间模型中经常被忽视.
多变量时间序列动态经常由复杂的,未知的部分微分方程 (PDEs) 控制,在各种科学和工程领域至关重要.

研究的目的:

提出一种新的连续时间模型,能够在多变量时间序列中学习未知部分微分方程 (PDE) 系统.
通过使用统一的框架,有效地纳入外源变量对目标序列预测的影响.

主要方法:

介绍了外源导向PDE网络 (EgPDE-Net),这是一个连续时间模型,通过自我注意和封闭的循环神经网络对PDE控制方程进行参数化.
开发了一种规范化策略,使PDE问题能够减少到一个可处理的,规范化的普通微分方程 (ODE) 数值解决方案问题.
启用任意步骤预测在任何时间点对多个未来值.

主要成果:

拟议的EgPDE-Net有效地模拟了外部变量之间的关系及其对目标序列的影响.
该模型实现了竞争力的准确性,通过在任意步骤预测中平均降低根平均平方误差 (RMSE) 9.85%和平均绝对误差 (MAE) 13.98%的平均值来优于强大的基线.

结论:

EgPDE-Net提供了一种强大而准确的方法,用于在多变量时间序列中学习未知的PDE系统,考虑外源变量动态.
该模型处理任意步骤预测的能力及其卓越的性能证明了其在复杂的科学领域推进时间序列预测的潜力.

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