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

• URL: http://arxiv.org/abs/2511.23307v1
• Date: Fri, 28 Nov 2025 16:06:24 GMT
• Title: Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems
• Authors: Enzo Nicolás Spotorno, Josafat Leal Filho, Antônio Augusto Fröhlich,
• Abstract summary: 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.<n>Second, we introduce the Projected HRPINN (PHRPINN), a novel extension that integrates a predict-project mechanism to strictly enforce algebraic invariants by design.<n>We validate HRPINN on a real-world battery prognostics DAE and evaluate PHRPINN on a suite of standard constrained benchmarks.
• Score: 0.5735035463793009
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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