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Learning Neural Differential Algebraic Equations via Operator Splitting

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arxiv 2403.12938 v3 pith:RBPLQ57Z submitted 2024-03-19 cs.LG

James Koch , Madelyn Shapiro , Himanshu Sharma , Draguna Vrabie , Jan Drgona This is my paper · ORCID
classification cs.LG
keywords algebraiccomponentsdifferentialdaesdataequationslearningmodeling
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. jaxdae: A JAX-native Differentiable Solver for Differential-Algebraic Equations in Coupled Multi-physics

    cs.MS 2026-07 conditional novelty 6.0 of 10

    jaxdae provides the first JAX-native differentiable DAE solver, using a frozen-grid BDF-2 replay adjoint for reverse-mode gradients and XLA-fused batched sweeps.

  2. Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraints

    cs.LG 2025-05 conditional novelty 5.0 of 10

    Manifold projection at each ODE step enforces algebraic constraints in neural ODEs, producing near-zero constraint violation and competitive long-horizon state accuracy on six benchmarks.

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