让神经网络自动满足化学反应质量守恒，还带不确定度估计。
Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modelling
- 用概率神经网络嵌入线性等式约束，保证物理规律符合度。
- 小数据下预测更准、不确定性更可信，约束满足率更高。
- 适合化工建模，尤其需要物理一致性与置信度的场景。
机器学习模型在化工过程建模中应用日益广泛，但常缺乏严谨的不确定性量化和物理规律强制机制。本文提出一种概率神经网络框架，在给定容差范围内确保线性等式约束的满足，同时捕捉随机不确定性。相比现有先进方法，该框架在数据量较少时表现出更优的预测精度、更好的不确定性校准效果以及更强的约束遵守能力；在大数据场景下也表现竞争力，且训练速度显著更快。我们在两个间歇反应器案例研究中验证了该方法，强制执行质量平衡约束。
原文摘要 · Abstract (English)
Machine learning models are increasingly used to model chemical process systems, yet they often lack principled uncertainty quantification and mechanisms to enforce physical constraints. We propose a probabilistic neural network framework that guarantees satisfaction of linear equality constraints within a given tolerance, while capturing aleatoric uncertainty. Compared to state-of-the-art methods, our formulation demonstrates improved predictive accuracy, uncertainty calibration, and adherence to constraints on reduced data. It also demonstrates competitive performance, but with significantly faster training times when evaluated on large data regimes. We evaluated this on two batch reactor case studies, enforcing mass balances.
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