Neural Differential Algebraic Equations

本文介绍了神经微分代数方程（NDAEs），适用于基于数据的微分代数方程建模。微分代数方程描述了同时满足微分和代数约束条件的系统的时间演化。特别感兴趣的是，包含其组成部分之间隐含关系的系统，例如守恒关系。该方法建立在通用微分方程的概念之上，即通过特定科学领域的理论构建为神经常微分方程系统的模型。本文展示了所提出的NDAEs抽象适用于相关的系统理论数据驱动建模任务。所呈现的例子包括（i）箱底动力学的反问题和（ii）泵、箱和管道网络的差异建模。我们的实验表明，该方法对噪声具有鲁棒性，并且具有外推能力，可以（i）学习系统组件及其相互作用物理行为和（ii）区分包含在系统中的数据趋势和机械关系。

Neural Differential-Algebraic Equations for Data-Driven Modeling of Systems with Implicit Relationships

The proposed methodology of Neural Differential-Algebraic Equations (NDAEs) is built upon the concept of the Universal Differential Equation, which involves constructing a model as a system of Neural Ordinary Differential Equations informed by theory from particular science domains.

The NDAEs abstraction is suitable for relevant system-theoretic data-driven modeling tasks, as demonstrated through experiments on the inverse problem of tank-manifold dynamics and discrepancy modeling of a network of pumps, tanks, and pipes. The proposed method is robust to noise and can learn the behaviors of the system components and their interaction physics while disambiguating between data trends and mechanistic relationships contained in the system.

Related works in this field include 'Learning differential equations for mechanistic modeling of biological systems' and 'Neural Ordinary Differential Equations for the Identification of Nonlinear Dynamic Systems'.