🤖 AI Summary
This work addresses the challenge that existing machine learning models struggle to effectively quantify uncertainty and incorporate physical constraints in chemical process modeling. We propose a novel probabilistic neural network framework that, for the first time, rigorously embeds linear equality constraints—such as mass conservation—directly into probabilistic modeling, guaranteeing predictions satisfy physical laws within a prescribed tolerance. The method simultaneously achieves well-calibrated uncertainty estimates and efficient training: in small-data regimes, it significantly improves prediction accuracy, constraint satisfaction, and uncertainty reliability; under large-scale data settings, it maintains performance advantages while substantially accelerating convergence.
📝 Abstract
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.