Physics-based Penalization for Hyperparameter Estimation in Gaussian Process Regression
Physics-based Penalization for Hyperparameter Estimation in Gaussian Process Regression
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DOI：
10.1016/j.compchemeng.2023.108320
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发表时间：
2023-06
期刊：
影响因子：
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通讯作者：
Jinhyeun Kim;Christopher Luettgen;K. Paynabar;Fani Boukouvala
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文献类型：
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作者：
Jinhyeun Kim;Christopher Luettgen;K. Paynabar;Fani Boukouvala
在高斯过程回归（GPR）中，通常通过最大化边际似然函数来估计超参数。然而，这种以数据为主导的超参数估计过程可能导致较差的外推性能，并且经常违反已知的物理特性，特别是在稀疏数据场景中。本文通过惩罚边际似然目标函数嵌入基于物理的知识，并研究了这种新目标对最优超参数一致性和探地雷达拟合质量的影响。提出了三个案例研究，其中基于物理的知识以线性偏微分方程（PDEs）的形式可用，而初始或边界条件尚不清楚，因此模型的直接正演模拟具有挑战性。结果表明，由增广的边际似然函数得到的新超参数集可以提高探地雷达的预测性能，减少对底层物理的违背，缓解过拟合问题。
In Gaussian Process Regression (GPR), hyperparameters are often estimated by maximizing the marginal likelihood function. However, this data-dominant hyperparameter estimation process can lead to poor extrapolation performance and often violates known physics, especially in sparse data scenarios. In this paper, we embed physics-based knowledge through penalization of the marginal likelihood objective function and study the effect of this new objective on consistency of optimal hyperparameters and quality of GPR fit. Three case studies are presented, where physics-based knowledge is available in the form of linear Partial Differential Equations (PDEs), while initial or boundary conditions are not known so direct forward simulation of the model is challenging. The results reveal that the new hyperparameter set obtained from the augmented marginal likelihood function can improve the prediction performance of GPR, reduce the violation of the underlying physics, and mitigate overfitting problems.