用贝叶斯方法嵌入线性约束，让模型预测更可信且符合物理规律。
Learning with Embedded Linear Equality Constraints via Variational Bayesian Inference
- 通过变分贝叶斯嵌入输入输出间的线性关系
- 在电池模型上显著缩小可信区间并减少约束违反
- 适合需要物理一致性与不确定性估计的科学建模
机器学习在科学与工程中应用日益广泛，但许多方法缺乏有意义的不确定性估计，且预测可能违背已知物理知识。本文提出一种贝叶斯框架，将输入与输出间的线性关系嵌入学习过程，同时对模型参数和领域知识提供完整的预测不确定性表征。我们在受电压与能量守恒约束的单粒子电池模型上评估该方法，结果表明其相比基于变分推断的标准贝叶斯神经网络，能显著缩小可信区间并减少约束违反。
原文摘要 · Abstract (English)
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.
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