论文标题
混合数据驱动物理学限制了高斯过程回归框架，并具有深内核的不确定性定量
A hybrid data driven-physics constrained Gaussian process regression framework with deep kernel for uncertainty quantification
论文作者
论文摘要
高斯工艺回归（GPR）一直是一种众所周知的机器学习方法，用于各种应用，例如不确定性量化（UQ）。但是，GPR本质上是一种数据驱动的方法，它需要足够大的数据集。如果可以合并适当的物理约束（例如，在部分微分方程中表达），则可以大大降低数据量并进一步提高准确性。在这项工作中，我们提出了一个混合数据驱动物理学限制了高斯过程回归框架。我们用Boltzmann-Gibbs分布编码物理知识，并通过最大似然（ML）方法得出我们的模型。我们采用深内核学习方法。提出的模型通过训练深神经网络从数据和物理限制中学习，该网络是GPR中协方差函数的一部分。提出的模型在高维问题中取得了良好的结果，并在提供的标记数据非常有限的情况下正确地传播了不确定性。
Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset. If appropriate physics constraints (e.g. expressed in partial differential equations) can be incorporated, the amount of data can be greatly reduced and the accuracy further improved. In this work, we propose a hybrid data driven-physics constrained Gaussian process regression framework. We encode the physics knowledge with Boltzmann-Gibbs distribution and derive our model through maximum likelihood (ML) approach. We apply deep kernel learning method. The proposed model learns from both data and physics constraints through the training of a deep neural network, which serves as part of the covariance function in GPR. The proposed model achieves good results in high-dimensional problem, and correctly propagate the uncertainty, with very limited labelled data provided.
