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

2026-06-02

AI Summary

This work addresses limitations in existing hybrid models concerning scalability, noise robustness, and complexity control by proposing a physics-encoded modular hybrid layer framework. The approach incrementally augments a baseline physics-based model with data-driven submodels, preserving previously acquired knowledge while theoretically guaranteeing that training error is monotonically non-increasing and convergent with respect to the number of submodels. Leveraging least-squares initialization, the framework effectively integrates physical priors with data-driven components. Evaluated on the nonlinear NARX benchmark and the Quanser Aero 2 platform, the method demonstrates substantially improved accuracy, generalization, and training stability compared to monolithic networks of comparable size, while maintaining interpretability and structural robustness.

Abstract

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.

Problem

• scalability
• robustness to noise
• model complexity
• hybrid models
• physical consistency

Innovation

• modular hybrid modeling
• physics-informed learning
• incremental model refinement
• monotonic error convergence
• scalable system identification