Differential-Algebraic Equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such as conservation relationships. Here, we present Neural Differential-Algebraic Equations (NDAEs) suitable for data-driven modeling of DAEs. This methodology is built upon the concept of the Universal Differential Equation; that is, a model constructed as a system of Neural Ordinary Differential Equations informed by theory from particular science domains. In this work, we show that the proposed NDAEs abstraction is suitable for relevant system-theoretic data-driven modeling tasks. Presented examples include (i) the inverse problem of tank-manifold dynamics and (ii) discrepancy modeling of a network of pumps, tanks, and pipes. Our experiments demonstrate the proposed method's robustness to noise and extrapolation ability to (i) learn the behaviors of the system components and their interaction physics and (ii) disambiguate between data trends and mechanistic relationships contained in the system.

翻译：微分代数方程（DAEs）描述了同时受微分约束与代数约束的系统随时间演化的规律。其中尤以包含分量间隐式关系（如守恒关系）的系统尤为重要。本文提出适用于DAEs数据驱动建模的神经微分代数方程（NDAEs）方法。该方法的构建基础是通用微分方程的概念，即通过结合特定科学领域理论构建的神经常微分方程系统。研究表明，本文提出的NDAEs抽象方法适用于相关系统论数据驱动建模任务。本文展示的案例包括：（i）水箱-歧管动力学反问题；（ii）泵-水箱-管道网络的差异建模。实验证明，该方法具备噪声鲁棒性和外推能力，能够：（i）学习系统组件的行为及其相互作用物理机制；（ii）区分数据趋势与系统内包含的机理关系。