Learning with Embedded Linear Equality Constraints via Variational Bayesian Inference
For engineers and scientists needing physically consistent predictions with uncertainty, this method improves constraint satisfaction over standard variational inference approaches.
The paper proposes a Bayesian framework that embeds linear equality constraints into learning to enforce physical knowledge, demonstrating reduced credible intervals and fewer constraint violations on a battery model compared to standard Bayesian neural networks.
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.