融合信息与机器学习的敏感性分析：利用物理知识与实验数据
Information fusion and machine learning for sensitivity analysis using physics knowledge and experimental data
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中文总结 AI 辅助
本文提出结合物理知识与实验数据的物理信息机器学习策略，构建DNN和GP模型并融入物理约束，经实例验证可提升全局敏感性分析的准确性。
中文摘要 AI 辅助
当计算模型（无论是基于物理的还是数据驱动的）用于工程系统的敏感性分析时，敏感性估计会受到模型的准确性和不确定性的影响。本文针对同时拥有基于物理的模型和实验观测数据的情况，研究全局敏感性分析（GSA），并探讨物理信息机器学习策略以有效结合这两种信息源，从而最大化敏感性估计的准确性。本文考虑两种代表性机器学习（ML）技术，即深度神经网络（DNN）和高斯过程（GP）建模，并研究在这些技术中融入物理知识的两种策略：（i）在ML模型中融入损失函数以强制满足物理约束；（ii）分别使用模拟数据和实验数据对ML模型进行预训练和更新。针对DNN和GP这两类模型，各构建四种不同的模型，并将这些模型的不确定性纳入Sobol指数计算。结果发现，与基于GP的模型相比，基于DNN的模型在模型参数和训练选项方面具有更多自由度，可使敏感性估计的边界更小。本文通过增材制造和湖泊温度建模实例对所提方法进行了说明。
英文摘要
When computational models (either physics-based or data-driven) are used for the sensitivity analysis of engineering systems, the sensitivity estimate is affected by the accuracy and uncertainty of the model. This paper considers global sensitivity analysis (GSA) for situations where both a physics-based model and experimental observations are available, and investigates physics-informed machine learning strategies to effectively combine the two sources of information in order to maximize the accuracy of the sensitivity estimate. Two representative machine learning (ML) techniques are considered, namely, deep neural networks (DNN) and Gaussian process (GP) modeling, and two strategies for incorporating physics knowledge within these techniques are investigated, namely: (i) incorporating loss functions in the ML models to enforce physics constraints, and (ii) pre-training and updating the ML model using simulation and experimental data respectively. Four different models are built for each type (DNN and GP), and the uncertainties in these models are included in the Sobol indices computation. The DNN-based models, with many degrees of freedom in terms of model parameters and training options, are found to result in smaller bounds on the sensitivity estimates when compared to the GP-based models. The proposed methods are illustrated for additive manufacturing and lake temperature modeling examples.
发表机构
- Vanderbilt University（范德堡大学）
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