Latent neural ordinary differential equations have been proven useful for learning non-linear dynamics of arbitrary sequences. In contrast with their mechanistic counterparts, the predictive accuracy of neural ODEs decreases over longer prediction horizons (Rubanova et al., 2019). To mitigate this issue, we propose disentangling dynamic states from time-invariant variables in a completely data-driven way, enabling robust neural ODE models that can generalize across different settings. We show that such variables can control the latent differential function and/or parameterize the mapping from latent variables to observations. By explicitly modeling the time-invariant variables, our framework enables the use of recent advances in representation learning. We demonstrate this by introducing a straightforward self-supervised objective that enhances the learning of these variables. The experiments on low-dimensional oscillating systems and video sequences reveal that our disentangled model achieves improved long-term predictions, when the training data involve sequence-specific factors of variation such as different rotational speeds, calligraphic styles, and friction constants.

翻译：潜在神经常微分方程已被证明对学习任意序列的非线性动态具有实用价值。与机械论模型不同，神经常微分方程的预测精度在较长预测时间范围内会下降（Rubanova et al., 2019）。为解决此问题，我们提出以完全数据驱动的方式将动态状态与时间不变变量解耦，从而构建能够跨不同设置泛化的鲁棒神经常微分方程模型。研究表明，此类变量可控制潜在微分函数和/或参数化从潜在变量到观测值的映射。通过显式建模时间不变变量，本框架可应用表征学习领域的最新进展。我们通过引入一种增强此类变量学习的直接自监督目标来证明这一点。在低维振荡系统与视频序列上的实验表明：当训练数据包含旋转速度、书法风格和摩擦常数等序列特异性变化因子时，所提出的解耦模型能够实现更优的长期预测。