将混合模型转化为神经符号系统,量化其不确定性并提升可解释性。
From Hybrid Mechanistic--Data-Driven Modeling Toward Neuro-Symbolic AI: What, Why, and How

- 用符号逻辑表达机制知识,学习模块作为信念,构建神经符号接口。
- 提出结构违反率与信念离散度,衡量模型对机制结构的遵守程度和不确定性。
- 在标签噪声和分布外场景下,提前识别模型可靠性,适合工业建模与安全关键应用。
融合第一性原理与数据驱动的混合模型在过程工程与科学机器学习中日益普及。现有设计多依赖架构与损失函数定义,缺乏跨领域可比性,且对机制部分的主观不确定性关注不足。本文通过将混合模型重构为神经符号(NeSy)接口,提出 Hybrid-to-NeSy(H2N)框架:将机制知识置于语言侧,学习模块作为信念侧,有效域与约束归入逻辑侧。该转换生成显式的神经符号推理函数与逻辑-信念分解。由此衍生两个指标:结构违反率(SVR)衡量学习信念是否符合机制结构;信念离散度(BD)反映学习置信度的集中程度,作为混合模型在机制部分的主观不确定性。案例研究显示,在标签噪声下的二分类任务中,高SVR与高BD模型在保留样本上表现更不稳定。在结构分布偏移时,H2N能提前量化模型外推不确定性,而测试准确率仅在事后揭示偏移。
原文摘要 · Abstract (English)
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.
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