Learning Neural Differential Algebraic Equations via Operator Splitting
This work addresses data-driven modeling challenges for systems with implicit constraints, such as conservation laws, but is incremental as it applies a known numerical method to a specific domain.
The paper tackles the problem of learning unknown components of differential algebraic equations (DAEs) from time-series data by proposing an Operator Splitting (OS) numerical integration scheme, demonstrating its robustness to noise and ability to extrapolate in tasks like inverse modeling of tank-manifold dynamics and discrepancy modeling of pump-tank-pipe networks.
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 laws. Here, we present an Operator Splitting (OS) numerical integration scheme for learning unknown components of DAEs from time-series data. In this work, we show that the proposed OS-based time-stepping scheme 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.