提出新方法让神经微分方程更稳定地处理长时序数据
A condensing approach to multiple shooting neural ordinary differential equation
- 用压缩法整合多段射击的约束条件
- 支持用Adam等一阶优化训练，效率更高
- 适合长期振荡轨迹建模，稳定性强
多段射击是一种常微分方程参数估计方法，将轨迹分割为小段独立积分，再通过等式约束消除前后段衔接间隙。相比单段射击，多段射击在处理高度振荡和长轨迹时更稳定。但在神经微分方程中，由于难以引入通用等式约束，该方法未被广泛应用。本文提出一种基于压缩的方案，在使用Adam等一阶优化方法训练多段射击神经微分方程（MS-NODE）时，有效融入射击等式约束，提升训练可行性与稳定性。
原文摘要 · Abstract (English)
Multiple-shooting is a parameter estimation approach for ordinary differential equations. In this approach, the trajectory is broken into small intervals, each of which can be integrated independently. Equality constraints are then applied to eliminate the shooting gap between the end of the previous trajectory and the start of the next trajectory. Unlike single-shooting, multiple-shooting is more stable, especially for highly oscillatory and long trajectories. In the context of neural ordinary differential equations, multiple-shooting is not widely used due to the challenge of incorporating general equality constraints. In this work, we propose a condensing-based approach to incorporate these shooting equality constraints while training a multiple-shooting neural ordinary differential equation (MS-NODE) using first-order optimization methods such as Adam.
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