Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems
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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911292389851136 |
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| author | Spotorno, Enzo Nicolás Filho, Josafat Leal Fröhlich, Antônio Augusto |
| author_facet | Spotorno, Enzo Nicolás Filho, Josafat Leal Fröhlich, Antônio Augusto |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_23307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems Spotorno, Enzo Nicolás Filho, Josafat Leal Fröhlich, Antônio Augusto Machine Learning Artificial Intelligence 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. |
| title | Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2511.23307 |