用平滑性约束提升科学参数估计，让机器学习不掩盖物理模型
Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation
- 基于损失曲面平坦性，避免模型过度复杂化
- 在多个数据集上准确恢复了科学模型参数
- 无需依赖具体网络结构，适合各类混合建模场景
混合建模将机器学习与科学数学模型结合，实现灵活且具备部分可解释性的数据驱动预测。然而，由于机器学习模型的灵活性，科学模型中的未知参数可能无法被正确估计，导致其在预测中被忽略。传统正则化方法虽可缓解此问题，但其形式通常依赖于模型架构和领域知识。本文提出一种架构无关的方法，在混合建模中同时学习并准确估计科学参数。核心思想是利用损失最小值的平坦性来实现模型简化，遵循奥卡姆剃刀原则。我们引入尖锐度感知最小化（Sharpness-Aware Minimization, SAM）并将其适配至混合建模框架。数值实验表明，基于SAM的混合模型学习能有效提升科学参数估计精度。
原文摘要 · Abstract (English)
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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