Title: Architecture-Agnostic Parameter Estimation via Sharpness-Aware Hybrid Model Learning

Abstract:

Hybrid modeling, which integrates machine learning algorithms with scientific mathematical frameworks, offers a balance of robustness, flexibility, and partial interpretability for data-driven predictions. Nevertheless, accurately estimating the unknown parameters within the scientific component remains challenging; the high flexibility of the machine learning segment may cause the scientific model to be effectively sidelined during prediction. While regularization techniques can mitigate this issue, their design usually relies heavily on specific model architectures and domain-specific insights. To address this, we introduce an architecture-agnostic approach for training hybrid models that ensures the proper estimation of scientific parameters. Our method leverages the Occam’s razor principle, utilizing the flatness of loss minima to promote model simplicity. Specifically, we adapt the concept of sharpness-aware minimization (SAM) to the context of hybrid modeling. Our numerical experiments confirm the efficacy of this SAM-based strategy in accurately estimating scientific parameters within hybrid models.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC