Hybrid modeling, the combination of machine learning models and scientific mathematical models, enables flexible and robust data-driven prediction with partial interpretability. However, the unknown parameters of the scientific model cannot necessarily be estimated properly, since the flexibility of the machine learning model might make the scientific model part effectively ignored in prediction. We may avoid it by applying some regularization, but the formulation of such regularizers typically depends on model architectures and domain knowledge. In this paper, we propose an architecture-agnostic method to learn hybrid models while properly estimating the scientific parameters. The idea is to use the flatness of loss minima to achieve model simplicity, based upon the Occam's razor principle. We employ the idea of sharpness-aware minimization and adapt it to the hybrid modeling setting. Numerical experiments demonstrate the effectiveness of the SAM-based hybrid model learning for scientific parameter estimation.

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