Title: PE-MHL: Physics-Encoded Modular Hybrid Layers for Scalable Learning of Complex Systems

Abstract:

Hybrid architectures that integrate physics-based principles with data-driven techniques have demonstrated significant promise in delivering both high accuracy and interpretability for control systems. Although recent advancements have improved the integration of physical consistency, issues regarding scalability, noise robustness, and the management of model complexity persist. To address these limitations, this study introduces the Physics-Encoded Modular Hybrid Layer (PE-MHL) framework. This approach incrementally enhances a foundational physics-based model by sequentially adding sub-models; each new module increases the model's capacity without erasing the knowledge acquired by earlier components.

We provide a theoretical foundation for this methodology, proving that when each new sub-model is initialized via least squares, the training error decreases monotonically as more sub-models are added, ensuring provable convergence. Experimental results from the Quanser Aero 2 platform and a nonlinear NARX benchmark indicate that PE-MHL surpasses monolithic networks of comparable size in terms of accuracy and generalization capabilities. Additionally, the framework exhibits more stable training dynamics and a superior ability to retain the intrinsic structures of the underlying data.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC