mlsanityData to 7 Oct 2026

Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems

arXiv 2511.23307 ↗First posted 28 Nov 2025cs.LG cs.AIcited by 3

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Abstract (arXiv)

This paper presents a framework for physics-informed learning in complex cyber-physical systems governed by differential equations with both unknown dynamics and algebraic invariants. First, we formalize the Hybrid Recurrent Physics-Informed Neural Network (HRPINN), a general-purpose architecture that embeds known physics as a hard structural constraint within a recurrent integrator to learn only residual dynamics. Second, we introduce the Projected HRPINN (PHRPINN), a novel extension that integrates a predict-project mechanism to strictly enforce algebraic invariants by design. The framework is supported by a theoretical analysis of its representational capacity. We validate HRPINN on a real-world battery prognostics DAE and evaluate PHRPINN on a suite of standard constrained benchmarks. The results demonstrate the framework's potential for achieving high accuracy and data efficiency, while also highlighting critical trade-offs between physical consistency, computational cost, and numerical stability, providing practical guidance for its deployment.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 13 of its 29 references that are in the map. First posted on arXiv 28 Nov 2025.

Builds on

13 of 29 references.

References · 13

  1. 2018Neural Ordinary Differential Equationscited by 3,733
  2. 2019Hamiltonian Neural Networkscited by 702
  3. 2017OptNet: Differentiable Optimization as a Layer in Neural Networkscited by 588
  4. 2020Lagrangian Neural Networkscited by 388
  5. 2020Universal Differential Equations for Scientific Machine Learningcited by 345
  6. 2020Fusing Physics-based and Deep Learning Models for Prognosticscited by 39
  7. 2022Deconstructing the Inductive Biases of Hamiltonian Neural Networkscited by 31
  8. 2024Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be?cited by 31
  9. 2021Constructing Neural Network-Based Models for Simulating Dynamical Systemscited by 29
  10. 2023Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraintscited by 15
  11. 2023MINN: Learning the dynamics of differential-algebraic equations and application to battery modelingcited by 10
  12. 2025Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraintscited by 4
1 more
  1. 2022The Executable Digital Twin: merging the digital and the physics worldscited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 3.

3 papers.

  1. 2026Empirical Stability Analysis of Kolmogorov-Arnold Networks in Hard-Constrained Recurrent Physics-Informed Discoverycited by 1
  2. 2026Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential-Algebraic Systemscited by 1
  3. 2026An Embedded RISC-V Evaluation of Kolmogorov--Arnold Networks in Hard-Constrained Recurrent Physics-Informed Modelscited by 0