Learning Neural Differential Algebraic Equations via Operator Splitting

James Koch, Madelyn Shapiro, Himanshu Sharma, Draguna Vrabie, Jan Drgona
3/19/2024
cs.LG

No official code found. Best implementation: pnnl/NeuralDAEs (20 stars, last commit 2025-07-24). 1 more below.

Abstract

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.

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Code Implementations(2)

pnnl/NeuralDAEsCommunity100%

Learning Neural Differential Algebraic Equations via Operator Splitting

202C++, CudaJan 16, 20241 years ago
drgona/NeuralDAEsCommunity57%

Learning Neural Differential Algebraic Equations via Operator Splitting

10CSS, HTMLJul 24, 20251 years ago

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Cite this paper

@article{koch2024learning,
  title  = {Learning Neural Differential Algebraic Equations via Operator Splitting},
  author = {James Koch and Madelyn Shapiro and Himanshu Sharma and Draguna Vrabie and Jan Drgona},
  year   = {2024},
  eprint = {2403.12938},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2403.12938v3}
}

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