让神经微分方程模型抗参数扰动，提升稳定性。
Control Disturbance Rejection in Neural ODEs
- 通过迭代训练，在不降低旧任务性能前提下更新参数。
- 在仿真中验证了对控制扰动的强鲁棒性。
- 适合需要稳定控制的动态系统建模场景。
本文提出一种用于神经微分方程（Neural ODEs）的迭代训练算法，使其对控制（参数）扰动具有鲁棒性。该方法基于先前的‘无遗忘调优’工作，以序列方式引入训练点，并在不降低已有任务性能的参数空间内更新参数。其核心创新在于：受平坦极小值概念启发，在无限维控制空间上求解非凸非凹泛函的极小极大问题。我们设计了一种投影梯度下降算法，适用于参数空间的无限维巴拿赫子空间结构。仿真结果表明，该方法能有效学习新数据点并增强对控制扰动的鲁棒性。
原文摘要 · Abstract (English)
In this paper, we propose an iterative training algorithm for Neural ODEs that provides models resilient to control (parameter) disturbances. The method builds on our earlier work Tuning without Forgetting-and similarly introduces training points sequentially, and updates the parameters on new data within the space of parameters that do not decrease performance on the previously learned training points-with the key difference that, inspired by the concept of flat minima, we solve a minimax problem for a non-convex non-concave functional over an infinite-dimensional control space. We develop a projected gradient descent algorithm on the space of parameters that admits the structure of an infinite-dimensional Banach subspace. We show through simulations that this formulation enables the model to effectively learn new data points and gain robustness against control disturbance.
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