Learning with Embedded Linear Equality Constraints via Variational Bayesian Inference

TL;DR

This paper introduces a Bayesian framework that embeds linear equality constraints into machine learning models, improving uncertainty quantification and adherence to physical laws.

Contribution

It presents a novel variational Bayesian inference method for incorporating linear equality constraints into predictive models.

Findings

Reduced credible intervals compared to standard Bayesian neural networks.

Lower constraint violations in the battery model learning task.

Effective uncertainty estimation respecting physical constraints.

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.