🤖 AI Summary
This work proposes a novel Bayesian framework that explicitly incorporates linear equality constraints—encoding known physical laws—into variational Bayesian inference, thereby jointly optimizing physical consistency and uncertainty quantification. By integrating Bayesian neural networks with a constraint-embedding mechanism, the method enables unified uncertainty modeling over both model parameters and domain knowledge. Evaluated on a single-particle battery modeling task, the approach significantly narrows predictive credible intervals and drastically reduces violations of the prescribed linear constraints compared to standard variational Bayesian neural networks, demonstrating its effectiveness and practical utility in delivering reliable, physics-informed predictions with well-calibrated uncertainty estimates.
📝 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.