论文标题
增强神经微分方程，以模拟未知的动态系统，并使用不完整的状态信息
Augmenting Neural Differential Equations to Model Unknown Dynamical Systems with Incomplete State Information
论文作者
论文摘要
神经常规微分方程用神经网替换常规颂歌的右侧，该神经网络可以借助通用近似定理来训练以表示任何函数。当我们不知道函数本身，而是具有ODE系统的状态轨迹（时间演变）时，我们仍然可以训练神经网以学习基础但未知颂歌的表示。但是，如果系统的状态不完全知道，则无法计算颂歌的右侧。传播系统的衍生物是不可用的。我们表明，当给出不完整的状态信息时，特殊增强的神经颂歌可以学习系统。作为一个有效的例子，我们将神经odes应用于3种，兔子，狼和熊的Lotka-Voltera问题。我们表明，即使删除了熊时间序列的数据，尽管缺少不完整的状态信息，但兔子和狼的剩余时间序列也足以学习动态系统。这是令人惊讶的，因为传统的ODE系统无法在没有完整状态作为输入的情况下输出正确的导数。我们在朱莉娅编程语言中实施了增强的神经ODE和微分方程求解器。
Neural Ordinary Differential Equations replace the right-hand side of a conventional ODE with a neural net, which by virtue of the universal approximation theorem, can be trained to the representation of any function. When we do not know the function itself, but have state trajectories (time evolution) of the ODE system we can still train the neural net to learn the representation of the underlying but unknown ODE. However if the state of the system is incompletely known then the right-hand side of the ODE cannot be calculated. The derivatives to propagate the system are unavailable. We show that a specially augmented Neural ODE can learn the system when given incomplete state information. As a worked example we apply neural ODEs to the Lotka-Voltera problem of 3 species, rabbits, wolves, and bears. We show that even when the data for the bear time series is removed the remaining time series of the rabbits and wolves is sufficient to learn the dynamical system despite the missing the incomplete state information. This is surprising since a conventional ODE system cannot output the correct derivatives without the full state as the input. We implement augmented neural ODEs and differential equation solvers in the julia programming language.
