发表机构
Institute for Computational Biomedicine, RWTH Aachen University; Center for Computational Life Sciences, RWTH Aachen University（计算生物医学研究所，亚琛工业大学; 计算生命科学中心，亚琛工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究旨在从混合机理-数据驱动建模迈向神经符号人工智能，核心方法是将混合建模设计重构为NeSy接口实例，即Hybrid-to-NeSy（H2N）转换，贡献是得出SVR和BD指标量化不确定性，通过案例研究验证了该方法的有效性。
AI 中文摘要
混合机理/数据驱动模型将第一原理与学习组件相结合，在过程工程和科学机器学习中越来越常用。常见的混合建模设计主要通过其架构和训练损失来指定，这为跨域比较或验证提供的共享语义接口有限，且对机理部分的认知不确定性关注较少。我们通过将这些设计重构为神经符号（NeSy）接口的实例，架起了混合建模与神经符号人工智能之间的桥梁。由此产生的Hybrid-to-NeSy（H2N）转换将机理知识置于语言端，学习模块置于信念端，有效性域和约束置于逻辑端。对于每个设计，H2N会产生一个明确的NeSy推理函数和逻辑-信念分解。基于此分解，我们得出两个指标：结构违反率（SVR），衡量学习到的信念是否尊重机理结构；信念离散度（BD），衡量学习到的似然性的集中程度，作为混合模型在其机理部分的认知不确定性。我们在一个有标签噪声的二元分类结构化混合模型的案例研究中实例化了H2N，结果表明，SVR和BD较高的模型在留出准确率上表现出更大的变异性。在结构分布转移下，H2N进一步量化了模型在外推过程中的不确定性，而测试准确率只能事后揭示相同的转移。
英文摘要
Hybrid mechanistic/data-driven models, which combine first-principles with learned components, are increasingly used in process engineering and scientific machine learning. Common hybrid modeling designs are specified primarily through their architectures and training losses, which offers a limited basis for a shared semantic interface to compare or verify them across domains, with comparatively little attention paid to epistemic uncertainty in the mechanistic part. We bridge hybrid modeling and neuro-symbolic (NeSy) AI by reconstructing these designs as instances of NeSy interface. The resulting translation, Hybrid-to-NeSy (H2N), places mechanistic knowledge on the language side, learned modules on the belief side, and validity domains together with constraints on the logic side. For each design, H2N then yields an explicit NeSy inference functional and a logic-belief decomposition. From this decomposition we derive two metrics: structural violation rate (SVR), measuring whether the learned belief respects the mechanistic structure; and belief dispersion (BD), measuring how concentrated the learned plausibility is, serving as a hybrid model's epistemic uncertainty in its mechanistic part. We instantiate H2N on a case study of a structured hybrid model for binary classification under label noise and show that models with higher SVR and BD exhibit greater variability in held-out accuracy. Under structural distribution shift, H2N further quantifies a model's uncertainty during extrapolations, whereas test accuracy reveals the same shift only post hoc.
