Leveraging Bayesian analysis to improve accuracy of approximate models
Leveraging Bayesian analysis to improve accuracy of approximate models
复制标题
利用贝叶斯分析提高近似模型的准确性
DOI：
10.1016/j.jcp.2019.05.015
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
D. Livescu
中科院分区：
文献类型：
--
作者：
B. Nadiga;C. Jiang;D. Livescu
我们专注于提高多尺度动力系统的近似模型的准确性，该模型使用一组参数依赖项来解释未解决或忽略的动态对解决尺度的影响。我们首先考虑各种方法校准和分析这样一个模型givena几个良好解决的模拟。在介绍了各种点估计的结果并讨论了它们的一些缺点之后，我们展示了（a）分层贝叶斯分析的潜力，以揭示近似模型中以前未预料到的物理依赖关系，以及（B）如何使用这些见解来改进模型。实际上，从贝叶斯分析中发现的参数依赖性被用于改进模型的结构方面。虽然我们选择在浮力驱动的变密度湍流闭合模型的背景下说明该过程，但该方法的统计性质使其更普遍适用。为了解决与程序相关的计算成本增加的问题，我们展示了使用基于神经网络的代理加速后验采样过程，并指出变分推理的最新发展作为一种替代方法，大大减轻了这种成本。我们的结论是，现代验证和不确定性量化技术，如我们认为有价值的作用，发挥近似模型的发展和改进。
We focus on improving the accuracy of an approximate model of a multiscale dynamical system that uses a set of parameter-dependent terms to account for the effects of unresolved or neglected dynamics on resolved scales. We start by considering various methods of calibrating and analyzing such a model givena fewwell-resolved simulations. After presenting results for various point estimates and discussing some of their shortcomings, we demonstrate (a) the potential of hierarchical Bayesian analysis to uncover previously unanticipated physical dependencies in the approximate model, and (b) how such insights can then be used to improve the model. In effect parametric dependencies found from the Bayesian analysis are used to improve structural aspects of the model. While we choose to illustrate the procedure in the context of a closure model for buoyancy-driven, variable-density turbulence, the statistical nature of the approach makes it more generally applicable. Towards addressing issues of increased computational cost associated with the procedure, we demonstrate the use of a neural network based surrogate in accelerating the posterior sampling process and point to recent developments in variational inference as an alternative methodology for greatly mitigating such costs. We conclude by suggesting that modern validation and uncertainty quantification techniques such as the ones we consider have a valuable role to play in the development and improvement of approximate models.
影响因子：
3.1
作者：
R. Plant;G. Craig
通讯作者：
R. Plant;G. Craig
影响因子：
1.5
作者：
Beskos, Alexandros;Pillai, Natesh;Stuart, Andrew
通讯作者：
Stuart, Andrew