通过模块化增量学习，让物理模型越学越准还稳定。
PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems
- 用模块化结构逐步添加数据驱动组件，保持已有知识
- 训练误差随模块增加单调下降，且理论保证收敛
- 适合需要高精度与可解释性的复杂系统建模任务
结合物理模型与数据驱动方法的混合模型在控制应用中展现出高精度与可解释性的潜力。然而，现有方法在可扩展性、抗噪声能力及模型复杂度控制方面仍存在挑战。本文提出物理编码模块化混合层（PE-MHL）框架，通过逐次添加子模型对基础物理模型进行增量优化，每个新组件在增加复杂度的同时保留先前学习内容。我们建立了理论保证：采用最小二乘初始化每新增子模型时，训练误差随子模型数量单调非增，并可证明收敛。在非线性NARX基准和Quanser Aero 2平台上的实证评估表明，PE-MHL在同等规模下优于单体网络，在精度与泛化性能上更优，同时具备更稳定的训练动态和更好的数据结构保留能力。
原文摘要 · Abstract (English)
Hybrid models that combine physics-based and data-driven components have shown strong potential for achieving accuracy and interpretability in control applications. While recent methods have made progress in incorporating physical consistency, challenges remain in scalability, robustness to noise, and control of model complexity. This paper proposes a Physics-Encoded Modular Hybrid Layer (PE-MHL) framework, in which a baseline physics-based model is incrementally refined through the addition of new sub-models, where each new component adds complexity while preserving what previous components have already learned. We establish a theoretical guarantee for this construction: with a least-squares initialization of each new sub-model, the training error is monotonically non-increasing in the number of sub-models and provably converges. Empirical evaluations on a nonlinear NARX benchmark and the Quanser Aero 2 platform demonstrate that PE-MHL outperforms equivalently sized monolithic networks in both accuracy and generalization, while also providing more stable training dynamics and better preservation of underlying data structures.
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