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.
@article{arxiv.2403.12938,
title = {Learning Neural Differential Algebraic Equations via Operator Splitting},
author = {James Koch and Madelyn Shapiro and Himanshu Sharma and Draguna Vrabie and Jan Drgona},
journal= {arXiv preprint arXiv:2403.12938},
year = {2025}
}
Comments
Updated version of the article now includes problem statement