将物理约束融入神经符号不确定性量化，提升科学预测可信度。
Constraint-Aware Neurosymbolic Uncertainty Quantification with Bayesian Deep Learning for Scientific Discovery
- 结合贝叶斯深度学习与可微符号推理，实现不确定性建模。
- 在材料与分子数据上降低34.7%校准误差，满足99.2%物理约束。
- 适合需要可解释、高可信科学预测的研究者使用。
科学人工智能应用需具备可信赖的不确定性估计并遵守领域约束。现有不确定性量化方法无法融入符号化科学知识，而神经符号方法则为确定性模型，缺乏严谨的不确定性建模。本文提出约束感知神经符号不确定性框架（CANUF），融合贝叶斯深度学习与可微符号推理。架构包含三部分：从文献自动提取约束、带变分推断的概率神经主干、可微约束满足层以保证物理一致性。在Materials Project（140,000+材料）、QM9分子性质及气候基准测试中，CANUF相较贝叶斯神经网络降低34.7%期望校准误差，同时保持99.2%约束满足率。消融实验显示，约束引导的再校准贡献18.3%性能提升，约束提取精度达91.4%。CANUF首次实现端到端可微管道，同步解决不确定性量化、约束满足与可解释性解释问题。
原文摘要 · Abstract (English)
Scientific Artificial Intelligence (AI) applications require models that deliver trustworthy uncertainty estimates while respecting domain constraints. Existing uncertainty quantification methods lack mechanisms to incorporate symbolic scientific knowledge, while neurosymbolic approaches operate deterministically without principled uncertainty modeling. We introduce the Constraint-Aware Neurosymbolic Uncertainty Framework (CANUF), unifying Bayesian deep learning with differentiable symbolic reasoning. The architecture comprises three components: automated constraint extraction from scientific literature, probabilistic neural backbone with variational inference, and differentiable constraint satisfaction layer ensuring physical consistency. Experiments on Materials Project (140,000+ materials), QM9 molecular properties, and climate benchmarks show CANUF reduces Expected Calibration Error by 34.7% versus Bayesian neural networks while maintaining 99.2% constraint satisfaction. Ablations reveal constraint-guided recalibration contributes 18.3% performance gain, with constraint extraction achieving 91.4% precision. CANUF provides the first end-to-end differentiable pipeline simultaneously addressing uncertainty quantification, constraint satisfaction, and interpretable explanations for scientific predictions.
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