Learning with Embedded Linear Equality Constraints via Variational Bayesian Inference
Abstract
Machine Learning is becoming more prevalent in science and engineering, but many approaches do not provide meaningful uncertainty estimates and predictions may also violate known physical knowledge. We propose a Bayesian framework to embed linear relationships across inputs and outputs into the learning process, whilst characterizing full predictive uncertainty over both the model parameters and the domain knowledge. We evaluated our method on learning the single particle battery model subject to voltage and energy balances, showing its ability to provide reduced credible intervals and constraint violations compared to standard Bayesian neural networks based on variational inference.
Cite
@article{arxiv.2604.24911,
title = {Learning with Embedded Linear Equality Constraints via Variational Bayesian Inference},
author = {Matthew Marsh and Benoît Chachuat and Antonio del Rio Chanona},
journal= {arXiv preprint arXiv:2604.24911},
year = {2026}
}
Comments
Part of the OPTIMAL: Optimisation and Post-Bayesian Inference in Machine Learning Workshop at AISTATS 2026