Neural Ordinary Differential Equations typically struggle to generalize to new dynamical behaviors created by parameter changes in the underlying system, even when the dynamics are close to previously seen behaviors. The issue gets worse when the changing parameters are unobserved, i.e., their value or influence is not directly measurable when collecting data. We introduce Neural Context Flow (NCF), a framework that encodes said unobserved parameters in a latent context vector as input to a vector field. NCFs leverage differentiability of the vector field with respect to the parameters, along with first-order Taylor expansion to allow any context vector to influence trajectories from other parameters. We validate our method and compare it to established Multi-Task and Meta-Learning alternatives, showing competitive performance in mean squared error for in-domain and out-of-distribution evaluation on the Lotka-Volterra, Glycolytic Oscillator, and Gray-Scott problems. This study holds practical implications for foundational models in science and related areas that benefit from conditional neural ODEs. Our code is openly available at https://github.com/ddrous/ncflow.

神经常微分方程通常难以推广到基础系统参数变化所创建的新动态行为，即使这些动态行为与先前观察到的行为相近。本文引入神经上下文流（NCF），一种将未观察到的参数编码成输入矢量场的潜在上下文向量的框架。NCF利用矢量场相对于参数的可微性，结合一阶泰勒展开，使得任何上下文向量都能影响其他参数的轨迹。我们验证了该方法，并将其与已建立的多任务和元学习方法进行了比较，结果表明在Lotka-Volterra、Glycolytic Oscillator和Gray-Scott问题的领域内和分布外评估中，均方误差上具有竞争力。本研究对于科学和相关领域的基础模型以及从条件神经常微分方程中受益的领域具有实际意义。我们的代码开放在此 https URL。

学习可泛化动态系统的神经上下文流