将物理约束嵌入神经网络，提升复杂系统建模的精度与效率
Hard-Constrained Neural Networks with Physics-Embedded Architecture for Residual Dynamics Learning and Invariant Enforcement in Cyber-Physical Systems
- 用递归结构硬性嵌入已知物理规律，只学习残差动态
- 提出预测-投影机制，确保代数不变量严格成立
- 适合需高物理一致性且数据稀缺的工业系统建模
本文针对由微分方程和代数不变量共同控制的复杂网络物理系统，提出一种物理信息学习框架。首先，构建通用架构——混合递归物理信息神经网络（HRPINN），通过在递归积分器中硬性嵌入已知物理规律，仅学习残差动力学。其次，提出新型扩展——投影式HRPINN（PHRPINN），引入预测-投影机制，从设计上严格保证代数不变量。框架具备理论表征能力分析支持。在真实电池寿命预测的DAE数据集上验证了HRPINN，在一系列标准约束基准上评估了PHRPINN。结果表明该框架在实现高精度与数据高效的同时，揭示了物理一致性、计算成本与数值稳定性间的关键权衡，为实际部署提供实用指导。
原文摘要 · Abstract (English)
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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