mlsanityData to 7 Oct 2026

Learning Neural Differential Algebraic Equations via Operator Splitting

arXiv 2403.12938 ↗First posted 19 Mar 2024cs.LGcited by 6

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 17 of its 42 references that are in the map. First posted on arXiv 19 Mar 2024.

Builds on

17 of 42 references.

References · 17

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5 more
  1. 2021Stochastic Physics-Informed Neural Ordinary Differential Equationscited by 19
  2. 2022Meta-Learning of Neural State-Space Models Using Data From Similar Systemscited by 11
  3. 2023MINN: Learning the dynamics of differential-algebraic equations and application to battery modelingcited by 10
  4. 2021Constrained Block Nonlinear Neural Dynamical Modelscited by 9
  5. 2022Structural Inference of Networked Dynamical Systems with Universal Differential Equationscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 4.

6 papers.

  1. 2025A Simultaneous Approach for Training Neural Differential-Algebraic Systems of Equationscited by 4
  2. 2025CHyLL: Learning Continuous Neural Representations of Hybrid Systemscited by 1
  3. 2026Learning Physical Operators using Neural Operatorscited by 1
  4. 2026Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systemscited by 1
  5. 2026HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEscited by 1
  6. 2026Learning to Test: Physics-Informed Representation for Dynamical Instability Detectioncited by 0