Learning model discrepancy: A Gaussian process and sampling-based approach

P. Gardner; T.J. Rogers; C. Lord; R.J. Barthorpe

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Learning model discrepancy: A Gaussian process and sampling-based approach

机译：学习模型差异：高斯过程和基于样品的方法

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摘要

Predicting events in the real world with a computer model (simulator) is challenging. Every simulator, to varying extents, has model discrepancy, a mismatch between real world observations and the simulator (given the 'true' parameters are known). Model discrepancy occurs for various reasons, including simplified or missing physics in the simulator, numerical approximations that are required to compute the simulator outputs, and the fact that assumptions in the simulator are not generally applicable to all real world contexts. The existence of model discrepancy is problematic for the engineer as performing calibration of the simulator will lead to biased parameter estimates, and the resulting simulator is unlikely to accurately predict (or even be valid for) various contexts of interest. This paper proposes an approach for inferring model discrepancy that overcomes non-identifiability problems associated with jointly inferring the simulator parameters along with the model discrepancy. Instead, the proposed procedure seeks to identify model discrepancy given some parameter distribution, which could come from a 'likelihood-free' approach that considers the presence of model discrepancy during calibration, such as Bayesian history matching. In this case, model discrepancy is inferred whilst marginalising out the uncertain simulator outputs via a sampling-based approach, therefore better reflecting the 'true' uncertainty associated with the model discrepancy. Verification of the approach is performed before a demonstration on an experiential case study, comprising a representative five storey building structure.

机译：通过计算机模型预测现实世界中的事件（模拟器）是具有挑战性的。每个模拟器到不同的范围，具有模型差异，真实世界观测和模拟器之间的不匹配（给定'真实'参数是已知的）。模型差异出现了各种原因，包括模拟器中的简化或遗失物理，计算模拟器输出所需的数值近似，以及模拟器中的假设通常不适用于所有现实世界的事实。模型差异的存在对于工程师来说是有问题的，因为模拟器的执行校准将导致偏置参数估计，并且所得到的模拟器不太可能准确地预测（甚至有效地用于）各种感兴趣的环境。本文提出了一种推断模型差异的方法，克服了与模型差异共同推断了模拟器参数相关的非可识别性问题。相反，所提出的过程旨在给出一些参数分布的模型差异，这可能来自于在校准期间考虑模型差异的存在的“可能的无似的”方法，例如贝叶斯历史匹配。在这种情况下，模型差异被推断出通过基于采样的方法来利用不确定的模拟器输出，因此更好地反映了与模型差异相关的“真实”的不确定性。在对经验研究的演示之前进行该方法的验证，包括代表性五层建筑结构。

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来源
《Mechanical systems and signal processing》 |2021年第5期|107381.1-107381.20|共20页
作者
P. Gardner; T.J. Rogers; C. Lord; R.J. Barthorpe;
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作者单位

Dynamics Research Group Department of Mechanical Engineering University of Sheffield Sheffield S1 3JD UK;

Dynamics Research Group Department of Mechanical Engineering University of Sheffield Sheffield S1 3JD UK;

Dynamics Research Group Department of Mechanical Engineering University of Sheffield Sheffield S1 3JD UK;

Dynamics Research Group Department of Mechanical Engineering University of Sheffield Sheffield S1 3JD UK;

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原文格式 PDF
正文语种 eng
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Model discrepancy; Gaussian process regression; Importance sampling; Bayesian history matching;

机译：模型差异;高斯过程回归;重要性抽样;贝叶斯历史匹配;

Learning model discrepancy: A Gaussian process and sampling-based approach

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