Neural Differential Algebraic Equations
James Koch Madelyn Shapiro Himanshu Sharma Draguna Vrabie Jan Drgona
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.