Embedding Linear Equality Constraints in Probabilistic Neural Networks for Dynamic Modelling
For chemical process systems, it enables physically constrained probabilistic modeling with better uncertainty quantification.
Proposed a probabilistic neural network framework that enforces linear equality constraints with a tolerance, improving predictive accuracy, uncertainty calibration, and constraint satisfaction on reduced data, while achieving faster training on large data.
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.